If said artificial wombs can produce healthy & physically normal children, at least as well as it can be done biologically, I don't see a problem with it.
How would we base the costs of this process, and who gets the bill?
To start out with, it would likely be an elective procedure with the patient paying the costs except in instances where there's a medical emergency which would have previously resulted in a miscarriage or a premature birth.
As it becomes a more common and accepted practice, it would likely evolve the same way that artificial insemination does. First, it was an elective procedure you pay for on your own, then insurance covers it if you have various conditions which result in problems conceiving and now there are a lot of calls to have it included in coverage for anyone who wants it. Artificial wombs would probably go down the same kind of path. First, they're a luxury, then a medical necessity for certain for various specific reasons, then just a basic service.