Is the situation that the Bitcoin network is coming dangerously close to having enough transactions to exceed that 1MB limit?
It is not, although the transaction rate is steadily increasing. The question is more about how Bitcoin should evolve, rather than imminent problems.
Bitcoin at its core is a notarization network using scarce tokens to prevent spam and data size limits against DoS. Relaxing the limit means more entries, which both helps with monetary use of these tokens as well as the their utilization for other purposes like asset transfers, dispute mediation, digital copyrights, etc. It also means more resource requirements for nodes, which could eventually lead to hobbyists getting out of the equation.
it seems like the people behind Bitcoin XT stand to make a lot of money if the big Bitcoin exchanges switch over to their version of the currency, so I'm not so sure.
It is open source software for a decentralized network, so at least there isn't a direct connection to developer revenue. Although, there is a lot of investment going on, and different companies stand to gain from different scaling approaches, which could have lead to conflicts of interest.