Long story short, DC editorial took a liking to him based on his work for their Vertigo imprint, and thought he'd be a good fit for Batman. The above cover convinced them he was the dude -- and no less than Marshall Rogers, of whom Jones remains a huge fan, vouched for him as well -- and Doug Moench wrote Red Rain specifically for Jones to draw. And thus Jones still draws Batman to this day, albeit mostly for miniseries projects in recent years (last year's Kings of Fear being the most recent).
Getting back to the "Troika" costume, Jones was the only artist on the Batman books who didn't mind the design, simply because he only cared that Batman's mask, cape and gloves remain the same, as those were the only things he felt people would see of Batman in the first place. ("Most people probably think he has bat feet," he said at the time.) It was Barry Kitson, Graham Nolan, and Tom Grummett who weren't too enthusiastic about the "Troika" suit, and it was Grummett who put Batman back into his old suit sans trunks in the story's last chapter. Truthfully, Kitson, Nolan, and Grummett's renditions of the "Troika" suit did look much better than Jones' but the suit still had the same issues regardless (too much gray/not enough blue, boot spines being a potential hindrance, the one-piece jammies look). Given how classic all three men's styles were and still are, I'm not surprised they wanted to get Batman back to a more traditional suit.
That said, Jones is best suited to stand-alone works like "Red Rain" where he can get as individualistic as he pleases, with total control over the characters and locations he depicts. It's not realistic to expect him to "play well with others" in the sense of an ongoing storyline starting with a chapter drawn by Jones, continuing with one by Grummett, then going back to Jones. Whatever world he's drawing, it's not the one the rest of us live in, or that anyone else can draw.
Also, BTW, that was a great period for Batman covers, with lots of strong entries by Brian Bolland, Michael Golden, Matt Wagner and others. Many, like the one above, were generic "pin ups" that had nothing in particular to do with the contents of the book, and could have landed on one issue as easily as the next. If they're ever released as a portfolio of prints, I'd bite.
While the suit still has the same design flaws, Nolan's depiction of it comes the closest to pulling it off and making it work as a viable Batman costume. Then again, he was pretty much the best artist on the Batman line at the time, so I would have expected nothing less. (Nothing against Tom Grummett, who I'm a big fan of, but his Bat-tenure would end an issue after "Troika" and he didn't find his groove on Batman himself until years after he left Robin behind.)