Interestingly, there are some very weird things that could happen with that rate.

An extreme example I know of is Xenopus oocyte maturation. Oocyte maturation goes through a number of steps, in one of those the oocyte basically hoards a whole bunch of mRNA but doesn't do much with it (for like days), then at the next stage it makes a whole lot of protein but little mRNA.

So in this (somewhat extreme) example calculating the rate of proteins made per transcript is going to yield very different answers, and is also going to obscure what is really going on in the cell.

This is an extreme example, but I'm sure you can see the difficulties.