So you'll end up taking a different route, most likely without you even noticing. You aren't forced to route through people with insufficient funds.
My point is that there simply might not be a route with enough funding.
This may be a valid point. But I suppose that it could be possible to send the money in smaller packets, one after the other. Or sending a part of the amount on one route and the rest on another one - most likely this would be the easier method, because in this case both partial payments could be managed simultaneously.
But I think that would be an exceptional situation and should be treated as one. LN isn't really made for big payments anyway. Most likely, the higher the payment amount, the harder it would be to find a "decentralized" route which evades the big nodes like exchanges or specialized LN hubs. So if people started to use it massively for big payments a more centralized structure could emerge. I would prefer instead to use sidechains for mid-to-large payments.