@OverTheRubicon
People here absolutely do live in another world when it comes to jobs - or maybe that's just what it's like in the public sector, or they haven't applied for anything for a long time?
- Barely anyone ever reads cover letters in the private sector (it's unlikely that it will even be a human doing the initial screen), so putting it there won't help
- In a huge number of jobs, telling your boss you want an interview is career suicide
- Lots of people have only 20 days leave and often need it to cover school.holidays
Personally I'd ask for 8am or similar and by Zoom for first rounds if possible, use leave if you can, and if not, make the excuse a dental appointment, because they legitimately often form a course of 2-4 sessions. If they won't be flexible then you'll otherwise be stuck forever.
Don't blame the public sector for the MN Job Fairyland scenario! In most public sector organisations these days, covering letters aren't requested - just an online application form. (And public sector tend to have minimum notice periods of at least 5 working days between invitation to interview and interview date.
From a public sector regular recruiter's POV: we will try to be flexible up to a point if a candidate can't make the original date/time offered, if we possibly can we'll offer an alternative slot and we'll interview over Teams or f-to-f, so long as we can make the process fair for all candidates not just the one in the OP's situation. But we're under pressure too; there's still the day job to be done while we're trying to run a recruitment, and getting all three members of the panel free to convene on another day within a reasonable amount of time from the specified interview date isn't always easy. Also we know that we'll end up carrying a vacancy - if we aren't already - as in 95% of cases even a standard recruitment, from drafting the advert to getting the person in post, takes longer to turn around than the outgoing employee's notice period, so we sometimes have to weigh up the risk of potentially missing out on a decent candidate versus dragging out the process even longer. Depending on the level at which the OP's applying, which based on her comments about the inflexibility of her workplace and what they feel entitled to know doesn't sound very senior, we could easily have 300+ applications for one post so if one out of the 6-9 candidates we invite for interview can't make it then harsh though it sounds, there will be plenty more fish in the sea (we always hold a reserve list of the 'next best' candidates to invite in case of drop outs in the run up to the interviews).
As for the PP who said interviewers should offer evening or weekend slots even though the business is 9-5...while the rare organisation may be able to accommodate that, recruiting managers and panel members are people with lives out of work too! My last interview panel was me as chair (carer to disabled DH out of work), panel member two (single mum), panel member three (young man planning his wedding). We don't get paid overtime and I already work the maximum permitted flexi hours every month over my contract so I'd be effectively interviewing for free. Sorry, but when there will be plenty of other promising candidates who can make a 9-5 interview slot...it's just bad luck if one person we'd have liked to see can't make what we're offering or a reasonable alternative that may be a slightly later date or a slightly earlier or later start time but still within 8-6 at best.
Sorry, this got quite long but it irritates me that so many MNers seem to live in some kind of parallel fantasy world where recruitment is concerned, and very rarely think of it from the perspective of the company hiring.
Anyway OP, it sounds like you've been unlucky with short notice invitations; hopefully future interviews will be more reasonable. You can ask for flexibility but be aware it may be beyond the interviews' gift to grant it. And as for your colleagues, you're just going to have to practice saying something like "I need leave/an hour off for a personal issue, it's too distressing to explain" and staying firm in the face of their nosiness. And definitely don't give up your job to seek another! That's crazy talk!