Well, I would never let MLB.tv be my source for the games. It always seems to be "buffering" right when there is a big play in game. Too unreliable. I have used it thru Apple TV, Roku, MLB.com, you name it. It is unreliable if you are a hardcore fan.
I have had it since day one several years ago, and I don't think I have ever seen a complete game from start to finish without any kind of interruption. There is always some sort of technical glitch between high internet traffic or their servers. It's good if you are out. But at home on a regular basis, I would not want it.
I consider myself a pretty hardcore fan and MLB.tv is great for me. I haven't seen the reliability issues you mention. The device I use it on most is my Apple TV (3rd gen 1080p version). I also use it with a PS3 and Roku in other rooms as well as an iPad. I have 30Mb Charter cable at home.
You don't need a connection that fast for reliable use though. I occasionally use it for day games on a spare computer at work. We only have 6Mb AT&T DSL there and it works fine in HD 95% of the time. Every once in a while it might drop to SD for a minute at work when I use the mosaic (4 games at once) feature but for watching one game it is solid HD.
I would say it is every bit as solid as Netflix and Amazon Prime.