Will a point be reached where the number of nominations tapers off around a certain number, or will World Heritage Sites continue to be nominated at a constant rate until the end of humanity?

Possibly a bit too far into the future to try to guess about!

But certainly for the next 30+ years it is difficult to see anything happening which would stop significant numbers of continued inscriptions each year.
What could possibly do so?
a. Lack of "good" candidates
There would seem to be plenty which, using the currently adopted criteria for inscription, are likely to meet the guidelines. The current T List, produced by States using their perception of what might succeed/has succeeded in the past, consists of 1632 sites. OK some will be found inadequate, but there are others which will be added. At an average 25 new inscriptions a year that could keep us going for at least another 60+ years!! Those with vague ambitions to see all or "most" WHS should reflect that this means they need to achieve a rate of addition of c25 sites pa just to "stand still" and that many geographical areas they might have thought they had "fully" covered might pop up again with a new inscription unless they also keep up with T List additions!!
b. A tightening of the Inscription Criteria
If anything, the entire direction seems to be against this. Whilst, on the face of it, inscription has become a far more "difficult" process than it was earlier with large amounts of money now having to be spent on nomination Files/Management plans etc, the net result doesn't seem to have been to result in more "nomination failures" (possibly just more "deferrals" unless circumvented by stroppy WHCs!). Every year "Creative" approaches to what constitutes "OUV" seem seem to extend the range of what is acceptable. Meanwhile, Heritage "professionals" and academics analyse and philosophise on the meaning of "Heritage" -forever broadening its scope! The passage of time also brings in "newer" cultural sites. Then the issue of "equal treatment" of all races and cultures makes it very difficult to exclude any! Furthermore the WHC seems to operate more and more as a political forum in which every interest group must be given a "share". It might be easier to achieve a brake in the number of Natural inscriptions since IUCN probably has an idea of where there might actually be a rational "target" for them I.e representation of all significant biomes - whereas the cultural aspects are far more open ended as far as ICOMOS is concerned? I know it also produced a "Gap analysis" but generally it seems to be on a less firm basis than IUCN's and also both ICOMOS and the WHC seems far more prepared to accept "near" duplicates - We can think of all those "Viticulture" sites!! Also, whilst it has been "policy" for both Natural and Cultural sites to try to fill "gaps" it never seems to have been policy to avoid (near) duplicates - as long as a reasonable "Comparison" case has been made out in the Nomination.
c. Informal Voluntary Reduction in Nominations
As stated above -the current T List gives plenty of "headroom" for the coming years but, conceivably there could be a movement among some State Parties to decide that they don't want to nominate any more (or at least as many as they currently do/recently have). Why might they want to do this? A public policy statement to the "World" that they already have their "fair share" of inscribed sites? A recognition that inscription brings a lot of problems and isn't worth the candle? There may be a few such countries but I can't see it making much difference to the overall rate of nominations. Indeed any "space" such countries might create in the maximum Annual nomination list seems likely to be filled immediately by countries who don't share such views. There are plenty of States who have a firm belief that they are not adequately represented! A few years ago the UK government tried to manipulate a situation whereby UK would not put forward anymore nominations (via a consultancy study which "demonstrated" that inscription wasn't "cost effective") -but it failed. WHS inscriptions are still seen as virility symbols of a country's status as a tourist destination, as an important cultural player and as a "good" conservationist
d. Change in Policy by UNESCO etc
The political inertia within such International organisations is enormous. One just has to look at how membership of the UN "Security council" still reflects a political settlement made in 1945! Can one really see UNESCO/The WHC agreeing that the "correct" number of sites has been inscribed or even that fewer should be inscribed each year? One possible driver could be a lack of money - the organisation already struggles and one might foresee a number of "rich" countries deciding to opt out/cut their contributions. I suspect that some other countries would fill the gap - at least as far as their own nominations were concerned - it wouldnt be that expensive relatively to for e.g China, India to make sure that they/their allies were still able to gain annual inscriptions. At best it could be that UNESCO/the WHC, faced with both financial problems and a groundswell that not enough is being done to preserve the sites already inscribed might make a change in policy towards spending a greater proportion of its income in trying to improve their preservation. But I doubt if any such change would ever be more than a slight alteration, as much for public consumption as for achieving any real change. In any case - what can UNESCO/WHC really do to improve protection/preservation beyond exhortation and political pressure - neither of which require large amounts of money.
e. Change in perception of the value of the WHS "Brand"
Currently the WHS "brand" is viewed very positively both among governments and among "ordinary" people (insofar as they have a view - but it appears they do have one when choosing where to visit and when a new site in their country is inscribed!). Could this change over time to less positive one? Already a third group of people - namely "conservationists" have some doubts - a recognition that inscription can actually have negative impacts through tourist numbers etc. The number of sites which are having to impose limits on numbers and on accessible areas is growing. Given the availability of such measures I can't really see this concern having much of an impact on future nominations. I might expect any such concern to be evidenced most by IUCN etc - they have other ways of/schemes for getting natural sites "protected" and may recommend these to their governments? Another possible aspect could be a "dilution of the brand" as more and more sites get inscribed. In a world where there are WHS "everywhere" its value decreases and countries/towns etc could become less likely to to want to put the money and effort into gaining yet another inscription. I would have thought that, in the eyes of most people and States, we are a very long way from that stage -and even a doubling/trebling of the number of inscribed sites over, say, the next 60 years would not achieve it. Indeed, conversely, it might be viewed that "WHS inscription" is almost the cost of entry to the "Club"- you can't really market your location as a serious destination if you are not "in"!
f. "Black Swan" events
By definition we can't foresee what these might be!! Major political, economic, societal or technological shifts/crises? But, from the above analysis, I would conclude that it would have to be under this heading that any significant reduction in the number of annual inscriptions would have to come about!!