Couldn't you make the exact same point of "where/what I want at the cheapest rate I want" for airline loyalty though? I mean, I know your point is "if" I want to stay in a specific place I don't want to have to book direct, but I would argue that

1) the reality is the immense majority of the suboptimal behaviour due to loyalty is not about booking channels but about booking an airline/hotel which is not the cheapest, most convenient, or best value for a given trip for loyalty and
2) it would be extremely paradoxical to make the case for BAH booking rather than hotels direct booking on the grounds that it would be silly to constrain yourself to a given booking channel.... which is precisely what booking your hotel through BAH imposes!

In terms of hotels loyalty, first of all, I would point out that the immense majority of large chains do not condition loyalty benefits to booking direct. That is the exception rather than the rule. Most have a constraint based instead on paying the brand or hotel directly, which means any paid at hotel (however booked) or any rate booked direct. Besides, not only have most hotel chains got best rate guarantees but in addition, unlike airlines, they typically give you an automatic loyalty discount (typically 5 to 10% off) when booking direct and often automatic discounts you cannot get through any other channel (e.g. 3rd night free, etc) .

So I take your point that in your case, none of your recent stays in a hotels from major brands have been booked direct since I don't know which hotels or brands, but conversely, I can promise you that with my own profile, there isn't a single case so far in 2025 where I could have booked the hotels I booked for cheaper by selecting a non-eligible rate, and most certainly not through BAH which apart from having limited options available is invariably more expensive than booking separately. I maintain top status with two loyalty brands and mid-tier with another two.

If I take the example of my hotels in May 2025, I had four hotel stays:

1) One of them i just went for an independent hotel rather than book at one of the brands that would have given me perks (despite plenty of choice available) since that's where I felt I could find the best value proposition for my need. That's not dissimilar to what I do with airlines, I'll look at where I am loyal but don't hesitate to pick outside to get a nonstop or a better rate or timing;

2) One of them I booked through a TA an eligible rate with special perks which gave me a third night free plus perks (breakfast, €100 hotel credit, upgrade, etc) and loyalty benefits (further upgrades, points etc). My total stay - which basically included the room, breakfasts, and enough credit for dinner each nice without paying a penny extra - cost a whisker above £300 for three nights in a 5* at the very heart of a major European city. The loyalty points that I received for this alone translate into €60 credit which I can use on absolutely any rate and any hotel in that brand (no need for special availability, no black out dates, etc -- compare that rate with avios earnings just for fun).

3) One of them I booked direct with the same hotel brand, again in what happens to be my favourite and regular hotel option in the heart of another major global city. I had booked two rooms each for about £180/night (5* hotel again) and both were upgraded to the two highest suites in the house (200 and 160 squared metres respectively) which each retail for well over £5000/night. And yes that also came with the breakfast, lounge access, late checkout and so on. The hotel was not full, there was no recovery for some random problem, that was just the hotel having those suites available and deciding to treat us to them (even on the second room which wasn't officially eligible to any perks). And again, with a total bill of just over £1000 for those two rooms and three nights, I received loyalty points which are worth over €200 which I can again use on any hotel and any rate.

4) Final one, different brand, cheap hotel about £60/night, very simple but very well located in the heart of a middle sized city, more points, booked direct for much cheaper than any website deal, breakfast and upgrade to a large corner room with a nice view and more points is more than good enough for me.

Now as you said, hotel loyalty may work for some and not for others just like airlines loyalty does, but on balance, I have to say that I personally find that typically, hotel loyalty is likely to work for far more people than airline loyalty. Of course, as you would with airlines, you need to make sure you pick it right (precisely, don't be lazy and let BA influence you into put your loyalty in Hilton which have a rubbish programme just because they send you that free diamond card with GGL, check the relevant fora on FT instead). Unlike airlines where you may be restricted by your own geography, hotels loyalty let you shop around or pick your favourite with generally global coverage (though of course they differ - so if you mostly travel in the US, then Starwood, Hyatt or Hilton will likely be best for you, whilst if you do a lot of travel in luxury in Asia, Shangri La might be a better bet, and if you want all range and include a variety of luxury levels and places including Europe, Asia and Oceania, Accor may be far better suited, etc)

Typically, the hotel loyalty automatically gets you the best rate available 95% of the time (if you pick a programme with a decent BRG), plus a further immediate discount of 5-10% which is typically best for most people, plus more generous rewards you can often use any time on anything (again, that depends on your programme) all that without status. status perks, well, we can discuss endlessly, but I'd argue that probably more people would be buying breakfast anyway if it wasn't included than would buy lounge access or seat assignment if it wasn't included. Of course, in both cases (hotels and airlines), one needs to be sufficiently careful and keep enough of a cold mind to check that they are really booking what's best for them and only using the loyalty as part of the equation and not as the primary decider (ie refraining from booking something which is not ideal just out of loyalty automatism) but again, there is really no reason why this should be any different - let alone worse - for hotel loyalty compared to airline one and certainly, I would find that defaulting to BAH to let your airline loyalty effectively decide on your hotel habits would most definitely be the worst of both worlds by any account (just like letting your hotel loyalty tell you which airline to fly or how to book it would be similarly counter-productive).