Blocking low-value pages frees crawl budget only where that budget is genuinely constrained, meaning a large site or one generating heavy crawl waste, and on a small site it does essentially nothing for budget because there was no constraint to relieve. The honest answer is a conditional yes: when crawl capacity is actually being spent on junk, removing the junk redirects crawling toward what matters; when capacity was never the bottleneck, blocking pages changes how much of what counts gets crawled by roughly zero. The pivot is whether your budget is truly tight in the first place, and most sites never need to ask.
On a constrained site, the logic holds and the gain is real. Google allocates a finite amount of crawling to a given site in a given window. If a large share of that allocation is being consumed by faceted-filter combinations, infinite parameter URLs, or other low-value churn, those visits are not reaching your important pages. Blocking the waste, through robots.txt disallow for whole patterns or by removing the links and traps that generate them, frees that capacity to flow toward the URLs you care about. Here, blocking-for-budget does what the advice promises.
On a small site, the same move is mostly theater. If Google can comfortably crawl your entire site many times over within its budget, your important pages are already being crawled as often as they merit. Blocking a handful of low-value pages does not give the rest more crawl attention, because they were never short on it. The budget was never the limiting factor, so relieving it relieves nothing.
This is why the universal version of the advice, block low-value pages to save crawl budget, misleads. Stated as a rule for everyone, it sends small-site owners chasing a benefit that does not exist for them, and it conflates a real large-site lever with a phantom one. Blocking pages may still be worth doing on a small site for other reasons, like controlling index bloat, but freeing crawl budget is not one of them.
Before you block anything to save budget, confirm a real constraint: check whether important pages are actually being crawled less often than they should, and whether crawl waste is genuinely high. If both are true, block the waste. If not, spend the effort elsewhere, because there is no budget there to free.