Why adult handwriting can improve
Adult handwriting usually deteriorated for an identifiable reason: speed was piled onto letterforms that were never fully automatic, a rushed grip became permanent, or decades of note-taking rewarded getting words down over forming them well. The good news hiding in that diagnosis is that none of those causes is ability. They are habits, and habits respond to the same process that created them: repetition, this time with attention.
Adults also hold two real advantages over children learning to write. You already know what every letter should look like, so all of your practice budget goes to the hand rather than the memory. And you can self-diagnose: you can look at a page of your own writing and see exactly which letters, joins, or spacing habits are doing the damage, then practise those specifically.
Messy adult handwriting is almost always trained-in habit: a grip that causes fatigue, letterforms simplified for speed, inconsistent sizing. Each one can be isolated and retrained.
Writing a full page at your usual pace rehearses your current habits. Five slow, attentive minutes on one specific movement changes them. This is the single biggest shift in method for adult learners.
Fixing the three or four letters that bother you most changes how a whole page reads. Adult improvement works best as a series of narrow targets, not a general resolution to write better.
Improvement happens at slow speed and transfers to full speed gradually. Returning to your normal pace too early is the most common reason adult practice fails to stick.