"Feasible"?? H*LL NO!!
It would be a commercial transmitter. This requires FCC 'type acceptance' or (in special cases) acceptance testing of the specific transmitter. Costs are in the high-5-to-middle-6-figures left of the decimal point.
A FCC station _license_ for that device would also be required. The costs for generating the supporting data needed for the license are 'non trivial', to put it mildly.
That's _before_ considering the 'design' costs of such a device. That's going to be _another_ high-5-to-middle-six-figure amount -- DESPITE the fact that you can use the basic design of a standard cell station. You have to have 'something' to replace the functionality for determining which cell answers a call, 'validating' the phone, managing inter-cell hand-off, etc. Even if you're not using the particular facilities for call management, you have to provide the basic 'control' functions to the cell station for *it* to operate properly. There's a *lot* of software to design/build/test, for 'emulating' the un-needed/un-used head-end functions required by a standard cell base-station.
Next, you've got the tooling and start-up costs for the production line to build the d*mn things.
Direct manufacturing cost is going to be in the low hundreds of dollars, *minimum*. Plus 'overhead' costs -- things like advertising, etc. Plus something towards recouping the 'development' costs mentioned above. Plus distributer/wholesaler mark-ups.
If you peg the total development/start-up cost at 'a few million dollars', you have to sell a few thousand of these devices a year, _at_a_PROFIT_ of over $100/unit, just to cover 'debt service' on the development costs.
Totalling: several hundred manufacturing cost, minimum $100 for debt service, plus 'something' towards retiring that debt, plus 'overhead' -- mgmt, marketing, etc., plus distribution costs -- I don't see _how_ such a device could carry a 'street' price much below $1,000 (probably _considerably_ higher). Considering that the buyer also has all the expenses of getting that FCC station license, I really question whether the sales of 'several thousand units/year' that the debt-service figure was predicated on is reachable. If the market is only 10 units/year, then you've got to get circa $10-25,000 per unit _just_ for the 'debt service'.
After all that, there is the 'minor' issue of how that base station 'knows' what the particular phone's "home network" _is_. and how to send the right 'magic incantations' associated therewith.
*AND* the matter of either 'co-ordinating' with the "real" cell-tower network so that call-handling is 'handed off' to this device, *or* of providing an over-riding signal such that the phone 'cannot see/hear' the real network when in range of this device. In the latter scenario, you have a *major* problem in ensuring that the "effect" of your base-station doesn't extend to anybody else's phones -- going by outside. (Not to mention the 'minor matter' of it being illegal to intentionally interfere with the transmissions of another licensed station. )*AND* the "problem" that arises when two people -- in adjacent apartments, say -- *both* try to install such a device. and one person finds that in half his apartment, he's "closer" to the other person's base station than he is to his _own_ station. Oh, yeah, their phones are both on the same 'real' carrier, so you can't even differentiate by 'home' network.
To make this idea "workable" -- in a theoretical sense -- you'd need to re-design the cell *phone* itself. with a separate "mode" of operation, where it locked up to this 'private' base-station, and made no attempt to query the "common-management" and/or use an alternate cell with a "better" signal.
If there is *one* thing that this 'crazy idea' is not, that thing is 'feasible'! "Feasible" means 'practical, from a _financial_ point' -- and 'finances' do look to be a real 'killer' for this project. Not the only one, but a killer nonetheless.