Sure, such user will need to open new channels quite often. But another, more regular, user who spends and earns more or less the same amount, will be able to use one channel much longer.
Most of the people I know tend to save some money every month (if not so dramatically), so I am afraid that's the typical case. And one can envision many more similar cases where the funding transaction is depleted.
A successful implementation of LN will surely place a much greater pressure on the blockchain even if a quite large portion of the transactions happen off-chain, so I am afraid the scalability problem of bitcoin still needs some more answers. Anyway, LN is an incredibly exciting technology with so much potential. No wonder the price of bitcoin is trending upwards with the news of SegWit and LN approaching.