Since the usual rule for poetry is to forbid long syllables next to each other and the stress is always on the "bles", we normally pronounce it "blest" before syllables that start with stress and "blessèd" before unstressed syllables. But "blessèd" can occur before unstressed syllables in tunes that include LSSL (the only examples I can find off the top of my head are "blessèd redeemer" and "blessèd are those/they/we" (huh, that's a really weird meter: LXSLSSLSXS/LSXSLSL times 4, except that the last is /LSLSXSLSL), and in both cases there are probably more hymns with "blest" before the words).
LSSL is often because of trochaic substitution (usually at the start of a line) or anapestic substitution (common anywhere, but the leading L means it can't be the start of the line here). Pure anapests (easy, but iambs are just so easy to reach for) or some kind of use of dactyl (not too hard, but even trochee is uncommon in the first place) are also viable. Other theoretical ways to construct LSSL are very rare in English (amphibrach sequences are common in some analyses, but I prefer to treat them as iamb + anapests + lone short, or even lone short + dactyles + trochee, because when speaking we strongly prefer to keep short syllables together).
If you see "reemerge", a fraction of your brain is wasted trying to think whether it should really be "remerge", but "reëmerge" clarifies itself immediately. And "coop" vs "coöp" is outright ambiguous however you try it.
The acute accent is probably more important - it forces a pronunciation change of the vowels, disambiguating "to resume" from "a résumé". Unfortunately there remain many heterophones without a standard accent placement ("minute" is horrible).
The grave accent is rarely needed outside of poetry; the only word I'm aware of that requires it is "learnèd" (adjective meaning "knowledgeable").