There is that popular provers which say, A drop of water can make an ocean. yes I believe is true because I gradually accumulated some SATs and now have move from being Satoshi owner to Bitcoin holder.
OP, you talked about patiently accumulating sats instead of waiting to buy a whole Bitcoin. It's a given that most users here may not even have owned a whole Bitcoin. Besides, the positive thing is to hodl and keep hodling as that shows support for Bitcoin. It shouldn't matter if it's not up to 1 BTC.
Yeah, the appropriate situation based on your story is when Bitcoin price is still cheap and faucet site can give you 1000-5000 Satoshis for every minute, if you claim it for everyday you can make a good living if you hold it until now.
I believe you're referring to the pre-2017 era. I read it was a glorious era for faucet claimers. I tried my hand on faucets too around 2017/2018 but my experience was far from encouraging. I don't know how many people still indulge it now as it seems to be a waste of time.