So you chose to ignore the alarms, not stick to planned times and not expect the totally obvious... its not remotely an excuse.
We all could just ignore stuff and not bother. I have good days and bad days with my disabilities:
On good days I spend 15-30 minutes and put on jeans/bra/t-shirt/blazer, pack handbag, brush/tie up hair, maybe a bit of eye shadow/mascara. I can look like a regular functioning member of society
On bad days (sometime I'm so bed I can't even function, similar to dementia patients my brain just literally won't 'think' in a bad state and its all basic muscle memory autopilot, I become a living zombie) I set and alarm or ask someone trusted to text. The soud will trigger action and I will just throw on a hoody over my leggings and vest/t-shirt I was wearing in the house, slip on ballet flats and go... takes 1 minute. No hair, no make up, you'll be lucky if I even have a bra on because I barely can move but I'm out the house. I might look like swamp thing but I'll be on time even with bare minimum functional skills.
I always try to prep in advance (handbag is kept packed, shower/wash hair on the night before I know I need to go out somewhere, wear 'lounge wear' thats passable in public in case I'm so bad I can't re-dress).
But I am never late, I could not just keep people waiting as its the height of rudeness and it can have consequences too. Like when you miss medical appointments it can effect not just you but others. It increases wait time as the appointment was wasted (when someone else could have used that time) and now they have to book you back in taking up another time etc... its just unfair to everyone.
I have never just thought 'oh, its past the time to go, I'll just finish this email, pack a bag and top up my hair and make up' (and those action show you have a physical awareness, thought process, energy and function too). At the point that its the time to go you just GO in any state you are in (well not naked, throw on pants if you can but the quickest you physically can regardless of if you 'feel pretty' the time to do that has passed).
It is exactly what infuriates people, when people knew an hour in advance and where prompted but they deliberately IGNORED it. They just sit around scrolling facebook etc... and wait until its time to leave the house and then just say 'oh, I'll just quickly pop in the shower', while they sit their munching a bowl of corkflakes they just made with ZERO urgency. There is no excuse for it, its a selfish choice that impacts on everyone waiting for you and shows no respect for their time.
People who are chronically late are always so blase about time and thats why they are always late, its behavioral not 'disability' and a lack of caring/want to change. Plenty of people with ADHD and other disabilities work on being on time, its a learned/trained action part of CBT just like its learned in everyone. It might require more alarms, pre-planning extra time or more concentration but its not just deliberately ignoring the plan you knew needed to be followed then using 'time blindness/ADHD' as an excuse.