Got a Question I can't answer
As with many other home improvement questions, the answer is: it depends.
It is not just the tub, you know. You gotta have a drain, with a trap, sloping towards a stack. Trap alone extends 4-5" (at least) below tub bottom. Oh, and if this is a remodel, you are looking at some heavy plumbing work - potentially having to move a wye fitting a foot or so down on the main stack.
Then, there is a question of house structure. In my house, joists ar 2x8, since house is not large. Some houses might have 2x10s. In my case, I could recess a tub only 3" or so into the floor before trap began intruding into the room below. Given that most tubs are at least 12" deep, recessing it even half-way into 2x10 framing is no trivial task.
Further, the question of support. Tubs are heavy, especially when filled with water and the bathing person. Sistered joists, heavy blocking etc are usually specced for locations where a tub is to be placed. Here, instead, you are going to be cuting a sizeable chunk out of at least one joist in order to recess the tub. You MUST provide adequate support.
For tubs installed over unheated basement/crawlspace, the other issue is insulation. You want at least R19 below the tub if you don't want your bath cold within 5 minutes on a winter day.
In other words, a properly installed sunken tub will heavily intrude upon whatever is below it. If this is a new construction, planning a closet on the floor below might be a good idea.