What do you set the limit to? What do you do when a router fails and your available bandwidth suddenly drops? All of the TCP end hosts will backoff properly and avoid melting the network with endless re-transmits. All of the TCP flows will converge towards sharing the available bandwidth, even if that is a moving target. Applying a congestion control algorithm on top of UDP like the other response says is fine. Perhaps TCP's specific congestion control scheme isn't what you need (it sucks at live video for example). But you really do need a congestion control algorithm.
I'd like to add to this by saying that the new congestion control algorithms ought to be "friendly" to TCP to avoid congestion collapse. Backing off by a factor smaller than 2, or increasing additively by a delta more than 1 MSS per RTT are all tricks that would cause harm to normal TCP flows.
Granted that TCP isn't really "fair" between flows that have different RTTs, one could really justify tuning their TCP behaviour. But the challenge is to do this _automatically_, which is what TCP has so successfully done for the past few decades.
EDIT: DCCP decouples congestion control from reliable delivery and its congestion control algorithms are TCP friendly.
