Yeah. Typically, you can find an OTA which is cheaper almost instantly. So you pay more for the points (and, potentially, the benefits).

Just as an example, often times major ITA's like hotels.com offer 10-15% cashback (e.g., 13% for hotels.com was available the day before yesterday). Sometimes, OTA like booking.com offer nonpublic rates that are ~15% cheaper than the direct rate (using Genius rebates and such).

Neither cash-back opportunities nor nonpublic rates are things you can leverage for a BRG. (I think BRG is mostly dead, anyhow. YMMV.) Heavily discounted rates from OTA like Ctrip which sometimes try to get rid of excess room inventory they bought can, potentially, be leveraged for a BRG claim. But, again, BRG claims have become a waste of time for the most part.

Besides, I think the most important issue in practice is that people which are invested in loyalty are less price-sensitive and much less likely to price-compare/shop around for the best offer. Lots of evidence to that effect. Instead, people invested in loyalty become more engaged within the context of the program (e.g., respond to program promos or engage with co-brands/loyalty program partners).