There has been a massive increase in the number of tourists to Myanmar and the price of accomodation has increased, no denying either of these. However, please realise that we are not talking Prague, Venice, Bangkok etc. number of tourists. Yes you will see other tourists at Inle, the main temples in Bagan and main sights in Mandalay and Yangon. However, you can still rent a bike and in Bagan for example and ride around for 4 hours from temple to temple without seeing a single tourist. Also the majority of tours seem to just do the big 4 so places outside those 4 are still relatively quiet.
Accomodation is harder to come by (which means phoning ahead, rather than just turning up in a place) and it costs a little more than it used to, but you can still get a room for $20 or less (hardly expensive compared to a lot of other non-SEA destinations. Food and transport is still cheap.
Personally I always advise people that want to visit to visit now, rather than wait. Although, I can understand the rationale of waiting (improved infrastructure, opening more of the country etc).