The internet doesn't have nodes that stop working if too many packets go through. Lightning nodes only work as long as they have enough liquidity to cover your transaction.
Remember that the lightning network actually doubled in capacity recently over a few months and that channels increase in size as the bitcoin price goes up. Meaning a channel with $2000 of capacity today will have ~$20,000 of capacity by the next halving (assuming we continue the 10x trend) without any changes.
This results is a decreasing failed transaction rate for increasing sizes of transactions as we move into the future.