I redeemed a (taxable) MF so that I could reinvest at a different co. It was not a retirement account, although it probably should have been as at the time I was contributing to it rather than a dedicated retirement fund. The amount is more than my max allowable contribution for my Roth.

I am behind in terms of retirement contributions.

Does it make sense to put this money into a taxable fund where my Roth is, transfer enough to get to my max contribution and then subsequent years, funnel the remainder into the Roth? Is there any reason why this would not be a good idea (other than the fact that it becomes locked away until retirement)?

It's not a bad idea as long as you keep saving on top of that transfer. If you let yourself think you're funding your Roth so you're moving ahead you'll get in trouble because you aren't moving ahead you're just moving money from pot A to pot B. You can't grow money that way, you have to keep adding to one pot or the other.