Here's my take on the situation.
We're on a shared server. On a shared server, no one client should consume more than their fare share of resources, such as disk space, memory, CPU time and bandwidth. If one client uses too much of any of these resources, it hurts the others.
MySQL connections use a lot of resources. If a client were allowed to use as many connections as they liked they would consume too many resources. Putting in a limit to the number of connections has the side effect of limiting resource use.
The problem we'd have going forward is that Phoenix might end up using more than $20/month of server resources while staying under our MySQL limit. If that's so, Steve (as rep of IH) will have an incentive to figure out another way to limit our usage to more closely match the amount we're paying.
A dedicated server solves this problem, since we're limited by the speed of the CPU and the amount of memory in the box. If we exceed those limits a little, the board just slows down. If we exceed them a lot, maybe the server crashes. Either way, only Buffistas is harmed. Our hosting service isn't going to kick us off, they don't care how often a dedicated server crashes.