I don't think this is a procedure that can just be written off the books, nor should it. You're missing the point that all indications are they did not fire Albie and instead let his contract expire - which likely happened at midnight last night. In fact, Albie is still listed as the head coach in BU's public employee directory that likely hasn't been updated since last week.
This means they open themselves up to a potential lawsuit if they name another head coach while he's still under contract. Of course none of us are aware of the terms of Albie's contract, but I don't imagine BU would sign off on exposing themselves like this.
If the contract expiration is what happened, where BU made the mistake was in their decision to just let it expire. Most likely, they either 1) stupidly refused to pay a small buyout for one month or 2) stupidly gave him a contract that doesn't prorate the buyout within the full year cycle (ie - the buyout would be the same on May 2, 2021 and April 29, 2022.)
I agree that letting this situation linger for a month is potentially detrimental to the program, at least in the perception amongst the fanbase ...what little is left. But the HR policy itself is not the problem, it's how BU approached the situation given a reasonable administrative policy.