One main barrier is not having a computer at home to be honest, trying to manage it all via the phone app. It is not just a few minutes a day, haha, that idea is funny
I don't have a computer at home - just phones and tablet - and I manage my emails on my phone easily within a few minutes every morning/evening because I have a system and deal with things daily and that is using a Yahoo mailbox app with very basic functions.
It will take you longer because you have a huge backlog that you are letting develop because you arent dealing with the emails regularly.
I did a massive detox/delete/filter etc around 5 years ago (spent an entire day on it and it was under 10,000 then - whoever thinks you can sort through 65,000 emails in half an hour is either deluded or The Doctor) but it clearly didn’t take and since having to rely on phone only it’s got ridiculous.
So 65K messages have come in in the last 5 years that you havent dealt with? Clearly the issue is the fact you dont have a reliable system or any sort of regular purging.
As for the time, yes it might take longer than 30 minutes to purge 65k emails, but you've let them build up for 5 years. You can do it in small chunks but you need to find a way to keep it under control or else any new email is just going to be as bad.
Start off by putting everything existing in a general folder, so your main inbox is empty so you can start from 0, but you can go through the old emails at your leisure.
Then every day commmit to spending 5 minutes keeping on top of your inbox. Skim the daily email and immediately delete junk - I go through, open anything I want to keep and then just highlight all "unread" emails and delete them enmass - and then file any important emails to your inbox folders set up in your organizing style. I have a general folder for Bills with sub folders for each category (water/energy/internet and phone etc) so if I just have 5 minutes I dump all bill emails in the general folder and then when I have more time I will go through and file them into the right sub folder.
This will prevent your new emails from getting out of control and allow you to deal with the backlog when you have a bit of extra time. It may still take more than half an hour to clear that but by spending 5 minutes a day keeping up with current emails then you aren't making the situation worse.
To deal with the backlog, it doesnt have to be done in one go, you can chip away at it in any small chunk of time you can find - the 10 minutes on the bus, the 5 minutes waiting for DC to come out of an activity, the couple of minutes of an ad break on a TV show etc.
Go to your backlog folder and the first email you see, search the company name/key word to bring up every email from them. If it is something important - bills/statements or things you need to keep - select them all and put them in a dedicated folder for that company/category. If it is junk then select them all and hit the delete button. Do the same for the next email, and the next until they're all dealt with. It will take time but this method will get rid of hundreds of emails at a time as you are breaking it down into groups of repetitive emails rather than trying to deal with each one individually.