I'm not sure raising the outbound fee of that channel would prevent any of this from happening. It sounds like the node operator should have set fees higher to cover the actual cost of draining their channels' liquidity.

One strategy is to open up large enough (and probably fewer) channels and set the fees such that if they're entirely depleted, opening and closing costs will be recouped. If the channel is depleted, it's done it's job, just open another.

Another is to dynamically adjust fees such that as liquidity becomes more scare in a channel, the fee rate (ppm) goes up. This naturally balances supply and demand. There are many plugins or node managers that will do this in an automated fashion, i.e. CLBoss.

There does seem to be a general equilibrium problem, where you can find the stables effective fees for your channels only to gain a peer (or even just liquidity with an existing peer) who has much greater demand for outbound liquidity and then your channels get saturated/depleted. Again, I think the only viable solutions are to completely automate channel fee management, or to set fees very conservatively.