People apply online right ? They could just forgo manual checks as needed...
Yes. That's one solution. A person at Service Canada needs to check over the worker's Record of Employment to see their wages and weeks/hours worked etc. and the reason for loss of work (people who quit aren't eligible). Those Records of Employment are documents, sometimes hand-written my employers, needed to be manually looked at.
As you say, one solution is to simply take the worker's word for it and calculate payments based on whatever they mark down on the online application and then pay out ASAP, and if there's any overpayments they can worry about collecting that later when this has all died down. Based on the Phoenix system debacle that will probably take years, but there's more important things right now.
Only problem is they aren't going to prosecute tens of thousands of people who lie on the application who say they got fired even if they actually quit, so they'd basically giving out free loans to tons of people LOL, but hey what's wrong with that given these times. Only other issue is a lot of people will just spend the money thinking they won't have tot pay it back, then later it will take a long time for the gov to get that money back.
Edit: the new emergency benefits program they introduced kinda just sounds like they're going to give out $2000 a month to everyone who have lost a job whether eligible for EI or not. I would think it would work where if you submit any kind of ROE they'll just give you the money. It's confusing so I'm not sure.