In short, the reason mech would benefit from an AA alternative to the viking is because of medivacs. Put simply, if terran is required to produce vikings pretty much all game for safety purposes, (or, indeed, banshees or ravens) then, unless one decides to build a second starport, they will not be producing medivacs. Yet the integration of medivacs into mech play through a second starport is problematic. The only time one would consider getting a second starport, at this point in WOL, is to bolster their AA force with ravens or extra viking production; not to produce medivacs.
Now why are medivacs so important? They add an interesting dynamic to the matchups through drop play and take attention away from death ball vs death ball engagements. Hellion drops, thor drops, siege tank drops - they're all cool to do and turn somewhat 'boring' units, like the Thor, into something that can be microed and positioned and exciting. Let's not forget that amazing moment in the MVP vs TOP finals when MVP did a mass mech drop in TOP's main on Daybreak, supplementing it with nukes on production facilities.
Late game mech vs mech, play like that might be somewhat viable...but count the amount of times it's happened. Count the amount of times we see thor drops, double siege tank drops, hellion drops past the early game in professional play. It's certainly not frequent.
The problem, currently, is that any attention mech pays towards medivacs, (aside from the single odd one) exposes it's already gaping AA weakness. A single viking or raven or banshee - let alone 2 or 3 - can make a huge difference in mech TvZ or TvT currently. In some instances it will be game-ending.
In mech TvT, the only reliable way to beat a superior viking count is to make more vikings. If one is lax with viking production, they die to air switches: see Ryung vs Yoda GSL Season 4 on Ohana. In mech TvZ, the instant one stops building 4/5 banshees, the zerg is likely on their way to hive tech - hence the need for ravens and vikings, (or an attack timing into a win or raven/viking transition). Could zerg be so ambitious with hive timings if the threat of runbys AND drops existed? Absolutely not. It would force a longer mid-game and a more interesting dynamic than the, 'rush to broordlord/corrupter/infestor' mentality that currently exists. With mech AA and medivac usage, that would, of course, still be possible but zerg would need more units to defend and terran would be safer vs the quick transition.
One issue would be making sure that vikings aren't made redundant in the face of mech AA but this doesn't seem particularly difficult. In TvT, why wouldn't you always want a couple of vikings at least to snipe drops or, in fact, to facilitate a complete air switch with strong AA, (as is the case now)? In TvZ, mech AA could suffer from similar weaknesses to the marine currently - it suffers damage from sieged up tanks and is blocked by broodlings. This alone seems to be enough incentive to want some vikings. Making the ground attack of mech AA the priority seems a good counter measure to people who don't want to overlap the viking and any mech AA unit. It would require target firing to bring down broodlords, (due to broodlings) or colossus, (because of their air/ground vulnerabilities). In effect, this makes them a good and accessible AA unit, but not the ideal. The ideal AA unit, in all instances requiring one, should be the viking.
One of the criticisms of mech AA suggestions might be 'does mech really need it'? We've seen, at least in WOL, a noticeable trend of raven/viking/bc in the late game to counter 'anti mech' broodlord/infestor corrupter. Furthermore, mech players are frequently seen beating bio players with a 200/200 timing, fending off drops with vikings or successfully competing in air warefare in TvT. On the face of it, then, one would have to say that mech does not require a factory based AA option.
On the other hand, HOTS intends to also introduce 'cool' new ideas into Starcraft 2. A factory based AA option, by my analysis, accomplishes just this. It not only introduces a new unit, with it's own specific role, but also makes another already existing unit of greater relevance in mechnical play. The unit need not be revolutionary or, in fact, interesting in itself but facilitating greater use of mechnical drop play - that seems cool.
Edit1: Corrected sentence.