Infinite precision intermediate arithmetic: how much would break?

The first problem is performance. Widening integer operations to i/u128 makes them way more expensive; widening float operations to ℝ will require extremely costly software calculations.

The second problem is that this is silently breaking a lot of code and there is basically no way to estimate the breakage; this is the worst kind of breakage.

But the worst of all is that C has shown that promotion rules are deeply unintuitive and confusing, and the vast majority of developers never understand them well. The current "no implicit conversions" policy is a very good idea even if it sometimes costs in extra characters. Performing implicit widening conversions is bad but acceptable; performing implicit narrowing conversions, like you suggest here, is a terrible idea.