With bitcoin a bigger block size would lower confirmation time and therefore make it more usable in everyday live.
No, it wouldn't. It would simply reduce the fee you need to pay to secure entry to the next block at times when the mempool is full, but it would make absolutely zero difference to the average block time and therefore the expected time for that next block to be mined.
If you want to reduce the confirmation time then you need to change consensus to aim for a lower difficulty. This doesn't solve the problem of making bitcoin "more usable in everyday life", though, since to have a block time low enough for point of sale transactions (i.e. a few seconds at most), you end up with frequent stale blocks and chain re-orgs, necessitating that you would have to wait for many more confirmations anyway.
You are right with what you say but I just meant that the average confirmation time would be quicker since many people just pay 1-2 sats/vByte and this transactions will also then get processed pretty quickly. Still it always depends of course on how crowded the network is and that at the moment is not a problem but could be one in the future. It was also planned to upgrade the block size by satoshi but since he disappeared it never happened.