It can depend on the hotel program and the hotels.

Different hotel programs have different relationships between hotel cash cost and hotel points cost.

A few of them like IHG and Hilton and Best Western now mostly (with some partial exceptions) make points cost roughly (but not exactly) proportional to cash cost.

But Marriott has historically priced points based on how many people redeem points for that hotel, not based on cash cost. So at Marriott expensive-on-cash hotels in place where hardly one redeems can sometimes be very cheap on points, and cheap-on-cash hotels in places where lots of people redeem (at other times of the year, perhaps) can sometimes be expensive on points.

Other programs where points are not all that related to cash cost include Choice Hotels and Wyndham Rewards.

And it depends what kinds of places you like to travel as to which programs are most important. If you like to travel to National Parks with only a small town near them, and you want to stay near the park, often those towns only have Choice, Wyndham, and/or Best Western, not the "big name" programs. For example, near the main entrance of Olympic National Park in Washington, there are only Choice and Wyndham hotels in terms of hotels you can redeem points for. Also only Choice and Best Western in Estes Park, Colorado, the nearest town to the main entrance to Rocky Mountains National Park. If you want to use other chain hotels, that may add an hour or two of travel in each direction, and you have to evaluate whether that is worth it (if you want to be in parks at sunrise, it may be much easier if you're close by).

On the other hand, if you're more into traveling to sizeable cities, most of the hotel programs will work.

And how to earn points may be different in different programs.

For example, in Choice, it's easier to pay for one-night stays in cheap hotels when they have a "stay twice earn 8000 points" promo like they tend to have twice a year, and/or to transfer from transferable programs. You don't earn that many points by signing up for the Choice credit card (it's good far a start, but you'll use those up quickly), so you have to earn Choice points through stays and/or ongoing spending, and/or transfers from transferable points programs.

On the other hand, there are several credit cards for each of the other hotel programs, so it's a bit easier to get a good head start by signing up for one of their credit cards when there's a good signup bonus, and then later signing up for a different card in the same program -- or in some cases upgrading, especially at Amex which offered me an upgrade points bonus from the bottom Hilton card to the middle Hilton card, and then later another upgrade points bonus from the middle Hilton card to the top Hilton card.

And another advantage to redeeming with Choice: At many Choice hotels, if one room is available on points, all rooms are available for the same number of points, even if some rooms are way more expensive on cash. So you might actually be able to get a better room with points than you would ever consider paying for, even if you might the least expensive room at the hotel affordable.

But beware a downside of huge multi-room "upgrades": If you care about having the room cool when you sleep, and you arrive late, it's much harder to cool down a hotel room that's broken up into multiple physical rooms than one compact room. The hotel rooms that have multiple physical rooms often have louse air conditioners, while the cheaper hotel room that one compact room often have better air conditioners. But even if they were the same, the bigger the area you have to cool, the longer it takes. So as senior who's found that I sleep better when the room is colder (around 66 or 67 F), I don't want upgrades to huge rooms any more. given that I often arrive at the hotel late.