Ah, so you are saying that I can use the same coin twice: once on each network. Basically, as long as the networks keep splitting the coins can be re-used. However, this would devalue the coin, independently of whether the new networks introduce further inflation. This seems undesirable to most people on all the networks: if by splitting I can still only buy 10 cups of coffee with my bitcoins, just now it's more of a pain because I have to remember through which network to use it, I wouldn't want to do it.

If someone started a new Bitcoin-like currency they should start from a blank slate. Cloning the network chains would be confusing and frivolous at best.