This is one of those things which are easier said than done. To start with, let me show you a picture of a four speed transmission which has been blown apart:
All of those hundreds of parts go through the front end of the transmission. If a single part is bad (which it usually is not the case), you have to pull all of this apart in order to diagnose and repair. Like the mechanic you talked to said, it doesn't make sense to replace just the part which is bad while you have it all apart. The parts are pretty much the cheap part of the rebuild (or fix). Why not just make it a brand new transmission through the rebuild process. You could replace the single part, at a cost difference of a couple hundred dollars, only to have it go bad again in the not too distant future when another part goes bad which wasn't replaced.
In most cases when a transmission needs repaired, it is one or more of the soft parts which have gone bad. These include the band(s) and clutches. Usually the hard parts, like the gears, do not go bad and are reused after a thorough cleaning and inspection. You also have to consider, the transmission is very susceptible to debris. When these soft part start letting go, it can put a lot of debris through the transmission which the filter cannot keep up with. When the debris starts going around, it will damage other soft parts in the process. Soft parts also tend to wear at about the same pace (within the same group). So, not just one clutch in the clutch pack will go bad, but the entire group of them will go bad. You aren't going to replace just one clutch, you have to replace all of them. One last thing to consider here is that they sell the transmission parts as a kit (with a few exceptions). You aren't just going to buy single parts. By parts in this instance I'm talking about the soft parts ... you can usually buy hard parts separately.
There is no other way, with current transmission design, for you to get at any of the parts inside the transmission ... at least the parts which make the vehicle go. The design as it is, is very compact and does the job very well. If there was any way for a mechanic to be able to get to the parts inside without going the way it does now, it wouldn't have the strength to stay together. Believe me when I say, you could be a rich man to design an automatic transmission to do as you are suggesting and still have it as compact and efficient as what is currently offered.
The reason you don't see a drain plug on most automatic transmission is because when you change the fluid, you also change the filter. The exception to this is when you take it to a shop and get the transmission flushed. When they do this, they force fluid backwards through your transmission using the cooling lines. This (supposedly) cleans the filter in the process as well as completely exchanges the old fluid for new fluid (to include the torque converter - which doesn't happen when you just drop the pan).
The reason for the cost, as you suggested, is because of one, the labor involved in removing the transmission from the car, and two, because not every mechanic can rebuild a transmission. To do it right takes some extra learning. You just cannot throw it together and expect it to work ... and every make/model is different. All of that costs money. Most engines, on the other hand, are pretty much the same (with a few exceptions). They are all pretty much hard parts which go together relatively easy. There are some idiosyncrasies, but for the most part, they're not a big deal.
I hope this gives you a flavor for why you aren't going to see too many shops offering to repair your transmission. Again, as the mechanic said, the major part of any transmission repair is the labor for Removal & Replacement of the transmission itself.