Although, to be fair, undecidability often does serve as a blanket "do not even bother attempting this" refusal. But having a semi-algorithm with a work limiter

Although, to be fair, undecidability often does serve as a blanket "do not even bother attempting this" refusal. But having a semi-algorithm with a work limiter bolted on ("if solution attempts take more than X operations and/or Y storage, declare failure") should often be pretty practical. After all, we already know of several theoretically exponential but practically linear problems.