An exchange usually makes more when people trade more ("we're in the moving business, not the storage business") and stocks are more volatile, so from one angle it would seem like the very worst place possible to try to encourage long-termism.

Why would I route orders through this exchange?

You could pay for the template-producing company to monitor the template-using ones, like an auditing company or any sort of certificate-issuing one.

It seems the companies on LTSE are not bound to be traded only there so it doesn't seem like the trading would mostly go through it, since it's bound to have less liquidity than traditional exchanges.