It seems like it would be pretty easy to make a REPL mode that did the big conversions automatically. Not sufficient to protect a naive user, but arbitrary precision floating point is never safe.
Care to expand on that? Are you advocating for interval arithmetic or maybe decimal floating point?
For what it's worth I think that one would rarely need to interactively deal with so much data at once that using, say, 10000 bit binary floating point would be prohibitive. It is difficult to lose the necessary significant digits with so much "safety margin", and one still has space for about a million of such high-precision floating point numbers.