I wouldn't turn it down if someone gave it to me, but I own two other Bigs-equipped guits. The standard Strat bridge is superior. ¯\_(ツ)_/¯
I think it depends on the guit that it's on. A Bigs really benefits from the high string angle between it and a bridge that you can generally only get on an archtop. On a flattop guitar, they're a tuning nightmare, even those that are supposedly designed for it. There just isn't enough break angle on the bridge and they slip easily. My Gretsch 5120 is pretty solid tuning-wise, but I have to restring my 5622 a bit differently to get the same stability since it's mounted too close to the bridge and has too much break angle when I run the strings under the roller. So yeah, they're a bit fidgety too and really need to be spec'd with the overall geometry of the guitar considered.
I can't speak for Joe, but it also depends on what you expect to get out of it, too. A Bigs isn't good for a sharp dive on any guitar, just some mild vibrato. Leo designed the Strat bridge to be an improvement over the Bigs and it definitely is in most ways. IMHO. YMMV. BRB. OMGWTFBBQ, and all that.
Yeah, that thing. It's similar on my 5622. I string it over the roller so the break angle isn't so severe, and that helps a lot. Gold hardware too... It looks good for about five minutes. Then it tarnishes and flakes, and just looks cheap.
You have a lever on your Strat bridge. That's all the arm is. Unless you don't use the trem at all and do it the same way this guy does:
I was quite happy to see this image as I had to have a Lester because of him. Made me feel good he had a Custom (even though it was - flawed) before the Standard.