Tarka's trying to be a manipulative Xanatos. I don't believe a word he says about friends and peaceful universes and all that. He probably wants to control the DMA for the power it will give him.
But, regardless of that, it seems other sources besides dilithium are few-and-far between, and they are not accessible to the general public. Starfleet, and Osyraa, may have had their hands on some good transwarp sources, but had to be reticent in their use. The Emerald Chain also rose to power over supplying dilithium (through slave labor it seems), and would rather halt (and crush) any research into dilithium alternatives for fear that it would disrupt its supply chain and authority.
I also think that they figured out a way to utilize dilithium directly for transgalactic travel (Delta Quadrant to Alpha Quadrant in days), and after that, their was a technological lull from the 26th century to the 31st century when time travel was the main source of technological breakthrough, and offered an easy source of transgalactic (and intergalactic) travel... i.e. taking the long way to get there and jumping backwards in time.
