1. Yes. I think it is good to use the shorter "La Tech" particularly during play by play. Louisiana has a needless 4 syllables. During pregame and recaps, I prefer Louisiana Tech, but don't mind La Tech.
2. The only negative I've ever heard was that it has a drawl. "LaaaaTech". I like the abbreviated version. I can't think of another school of note that uses a 6 syllable word as it's only identifier. Maybe Air Force Academy... Still, I would put it as the late great Mitch Hedberg would probably put it: "It's time to embrace the abbreviation".
Heh. Pennsylvania State. That doesn't sound right at all.
Also, I like the identity that La Tech gives better than LTU. Just look at our helmet. Even if someone has never heard of our school, they know who the helmet belongs to. I've switched onto a basketball game that was being televised and it took me a second to realize it was the right game since the scoreboard was using LTU.
3. I think Louisiana Tech has already committed itself to LA Tech and just doesn't know it yet. As Jay said, it was used for latech.edu and latechsports.com. When these are verbalized, it's "La Tech dot e. d. u." not "l. a. Tech dot e. d. u.". The significance of the national media using this and not Tech is that the national media has a better handle on what the nation is referring to us as. They probably did not create LA Tech, they probably picked up on it. I think the fact that Louisiana Tech the university hasn't been using this shows either strict brand protection or a disconnect from the masses. I think that they stand very little to lose by adopting La Tech.
4. When I am in south Louisiana, most of the time Louisiana Tech is referred to as LA Tech. I see no negatives associated with the adoption of La Tech. I do not think it weakens branding. Any time a change is introduced some people in the fan base will react negatively. However, I don't see most of the fan base being bothered by this. Many fans use it occasionally already. If anything this would represent some positive change and obvious proof that someone is paying attention to the marketing of Louisiana Tech athletics, so even if they don't like the change, they like what the change represents.