I'd agree with the idea of getting rid of Bastion Points, and gating based on gold does seem like a decent approach, though it would take a lot of time to really figure out the details. We wouldn't want it to be too overly-finicky.
I've run an experimental build of a Bastion (a residence growing into a manor house), and I'm now thinking my earlier ideas of stacking facilities into progressing tiers isn't really needed, though some basic growth in functionality within each facility might be useful.
So my current thought: You start off with 4 basic facilities (3 roomy, 1 cramped) that you can design as you wish. You can then spend gold to buy more basic facilities, or upgrade a basic facility to a special facility, with the amount you spend determining what benefits you gain from it.
As a spitball approximation (based on the Level Up wealth progression table), I'd look at the cost of developing the special features of the facilities as something like:
Level 5: 500 GP
Level 9: 2,500 GP
Level 13: 8,000 GP
Level 17: 30,000 GP
For example, you might start your Bastion from a broken-down inn. You make one of the rooms and maybe a kitchen functional for personal use, and clean up the bar and stable to act as special facilities (500 GP each).
Then the bar can get the UA Storehouse functionality (essentially 50 GP earned per week of operation), while the stable helps keep your mounts healthy. (Heal injuries, temp HP, faster travel pace for the next week? Figure out a few minor benefits.)
If you pay to upgrade them at level 9, the stable gets the benefit of properly training your mounts (advantage on Animal Handling checks) and a professional reputation that allows you to buy and sell mounts for a profit. The pub, meanwhile, starts attracting "regulars" that act as the start of an information network.
In general, special facilities should be able to keep performing their function, regardless of whether you're there to give orders. The pub keeps running and making money even when you're out of town. This is partly because I'm assuming no Bastion Points, and partly because you paid to get the special facility, so it shouldn't be spending a lot of its time non-functional.
That wouldn't apply for things like research actions, of course, since the point of that is you having something specific you want information on, and if you're not there, you can't easily tell them. (Unless there's some sort of "communication" facility or upgrade.)
With no Bastion Points, there's no "free" magic items or resurrection. However there should be facilities that can craft magic items (common/uncommon/rare/very rare at levels 5, 9, 13, and 17, respectively), and maybe a small temple that can provide a periodic no-cost resurrection (you still have to get your body there, though).