Matrix as a protocol is neither bloated or slow, and ~32.1M folks have managed to use it successfully, directly or indirectly, as a global chat network. Presumably that counts as a 'large network'; it's certainly bigger than Freenode.
Synapse as an implementation has historically been bloated, but it's been steadily improving (and in fact last week's Matrix Live has a fascinating analysis of how the remaining memory usage is being fixed: https://youtu.be/694VuhmVmfo). Meanwhile implementations like Dendrite & Conduit are positively skinny.