Again, an unrealistic scenario.
I (like most users) don't get paid$ 10 many times over the course of a month. I usually only pay$10. After 10 payments, my channel will be reset to zero. And you will need to either re-create the channel, or replenish it using a third-party service. And this is the fee for an additional on-chain transaction.
I'll try a more realistic one: how about you get $1000 salary once a month, and pay your normal bills with it? Bills will go from high amounts like your rent to daily small amounts for coffee. Then you indeed can't use the same funds several times. It becomes slightly better if you receive your salary every week. You probably don't want an open channel with your employer (I wouldn't want them to know my remaining balance), so you'll still need a third party.I (like most users) don't get paid$ 10 many times over the course of a month. I usually only pay$10. After 10 payments, my channel will be reset to zero. And you will need to either re-create the channel, or replenish it using a third-party service. And this is the fee for an additional on-chain transaction.
I have some funds in a Blue wallet that I don't mind exchangeing 1:1 for on-chain funds - (you) pay the TX fees on your end and I do likewise. Having no funds on your end is good as it enables you to have inbound capacity when you open a new channel.
Just an aside for a previous comment in the thread:
If you have 1 BTC, wouldn't it be better to open 10 X 0.1 channels, or even 100 X 0.01 channels which would make you a mini-hub that others could then start connecting to?