An if-like conditional construct will not, by itself, re-evaluate the condition when an exception occurs, unless it is a special exception-aware construct (a weird macro someone made). The conditional construct would itself have to have an internal restart point around the conditional expression, which intercepts the exception.

"Condition" is just a silly name for "exception". It does not mean "restartable exception". It's a terminology that Common Lisp copied from PL/I. At the time Common Lisp was being standardized, it was not a common programming language feature, so the naming didn't matter. In the decades since, the world went to "exception".

The word "condition" already has a clear meaning in computing, referring to a logical state ("condition control register", "conditional branch", ...). The "condition variable" synchronization primitive (which has no condition-like state!) is bad enough; we don't need to heap more meanings on those words.

Note that processor instruction sets have exceptions, precisely restartable, down to the instruction, without requiring a cooperating restart point. E.g. any code can hit a page fault: the exception handling will fix it up, making a page present at the faulting address, and then restart the instruction that faulted.