At best, expect them to be late or within a few days from your deadline. At worst, follow up and be emotionally prepared to get ghosted.
As much as I give everyone the benefit of the doubt, I also acknowledge nobody cares about my hopes and dreams the way I do.
Some people will put your deadline on their calendar, if they really like you. Most, though, will wait until the deadline has come and gone and expect that you will follow up with them. You can tell because they'll already be late and be rushed to dig through their e-mail looking for the core competencies and primary app you sent them months ago.
Some are willing to keep their word, others will let the e-mail get buried in their inbox, others still will be so overwhelmed with (gesturing broadly) all of this going on in the world and will just not have the bandwidth to write you a letter, even if they do like you.
Funding is going away and people are being fired. If your school suffers from the trends toward adjunctification, all the more precarious. Everyone with a PhD is sweating right now. This is so not what they printed in the brochures when they were considering grad school.
And this one is just the cynic in me wanting to bash the cymbals, but...especially today in the academy, there is a growing resentment toward professional training programs because the education itself depends on the work of the academy, but their work is being actively defunded and undervalued. Meanwhile, graduates of professional training programs are compensated very well with reasonable job security, and students are willing to pay a pretty penny for training. The economic incentive toward practice over theory makes it seem like anyone who wants to be a physician (but is intelligent enough to go to graduate school) is "selling out."
I have absolutely seen this logic working against my peers, for example, working under PIs that don't let pre-meds publish because "they don't really need it like the PhD-hopefuls do." Obviously it's not something anyone will own up to in polite company, but it's a bias that makes sense based on the way the system is structured and the very recent attacks on higher education. Something to be aware of.
