On the one hand, I've always felt that this was a bit of an odd oversight on Hyatt's part (since there's likely to be a subset of folks who end up "living" in hotels because of aggressive travel schedules).

On the other hand, that is a very small subset of folks in most years, owing to Hyatt's smaller footprint than Marriott, etc. It will probably be a bit larger this year, since at least some folks probably came sailing into 2021 with 20+ nights carried over from 2020 and then got double-credit on another 20 in the first part of 2021 (this is hardly crazy if you, say, visited family over both holidays but opted for hotel stays...a week at Christmas and a long weekend at Thanksgiving easily gets you to a dozen from 2020, for example), but it is still an outlier and it feels odd to "stop" nudging folks at that level (or to weaken the nudge on folks who know they're likely to overshoot...if someone knows they're going to be in hotels for, say, 125-140 nights/year [there's a subset of road warriors who do this, and it is also not hard to imagine folks doing lower-yield long stays in nicer places in the off-season] this is potentially the difference between developing them as a "captive" and them deciding to focus on two sets of status).

I feel like the "right" answer would be to just issue a flat 500-1000 points/night past 100 nights or throw in some other persistent "goodie" for the rest of the year...maybe free parking on paid stays? :-p.

Honestly, I think this set of folks falls into two categories. The first is folks who end up "parking" at a small number of hotels (e.g. the guy who spends a week per month on a business trip in the same city and thereby has 12 Sunday-Saturday stays (72 nights)). In these cases, I'd argue that the onus is at least partly on the hotel to arrange some odd-and-end benefits (maybe some reduced-cost or complementary laundry or reduced-cost parking) since that much business does give the traveler a bit of negotiating power. The other is folks who bounce around a lot (i.e. 10 nights in FL, 10 in Los Angeles, 10 in New York, etc. throughout the year) and thereby manage to hit like 30-50 hotels in the process. There's not much that's going to pop out on the hotel side...so my joke about free parking aside, working to ease some costs on this front (parking, laundry, etc.) would probably be the best option if points and so on aren't on offer. The issue here is that those areas are often profit centers for your higher-end hotels, and I suspect that even when they would do so to land a "whale" at their property, they'd be reticent to give more ground, period, on folks only spending a few passing nights.

(To be fair to Hyatt, IIRC prior to the transition from Hyatt Gold Passport to World of Hyatt the four sets of ten-night awards weren't there...Hyatt's footprint at the time was smaller and had enough holes in it that they were alongside Starwood in it being tricky to put all of your nights with them and I think they sort-of acknowledged that folks doing lots of travel would need to split their business...hence the top tier being 60 nights instead of 75 or 100.)

Edit: I probably should have thrown in the asterisk that folks with the CC and driving spend over it can also easily take 10-15 nights off of these requirements, and can potentially knock even more off under the right circumstances. Also, I'd note that this creates an odd sweet spot for diverting CC spend: If you run $25,000 over the CC, you get ten nights, which equates to one 10-night award slug...a 10,000 point bonus for spending $25,000 is not a trivial bonus in terms of Hyatt points. But the lack of anything past 100 nights partly inverts that, too.