Nothing will happen if the network get too big and from what I observe, the network also keeps increasing every year, I don't think it's always the same number of transaction every year. I don't have too much knowledge about Bitcoin tech but with the little knowledge I have, what can slow Bitcoin transaction speed is when you pay a very low amount sat as fee, miners will select transactions with high fee and process them first before that of people with low fee, I read that somewhere. If transaction fee is normal, then speed will not be a problem.