I'll read the study at a later time - simply don't have time at the moment. The Heritage foundation is a bit sketchy, as pointed out, but that doesn't mean their methodology is without merit and I'm curious to read it.
That being said, immediate tangible benefits from unions aside, we're on the verge of a significantly changing work environment and without unions the workers don't have a voice or any significant bargaining power. Even if the status quo isn't horrible for workers - a point worth arguing both ways - what happens in ten years, twenty years, when automation does kick in more, when there is some significant change, who's going to bat for the regular worker if not unions? We can't entirely predict what's coming and unions need to be present to help the worker bargain with the times and keep conditions favourable for the working class.
This all being the case though, unions need to trim the fat. The model of unions that kicked around decades ago just doesn't cut it in today's world. The unions are a means by which the workers can unify and use their collective power to strike back at a changing world, but unions aren't the only game in town and unions need to stop acting like it and learn to roll with the punches a little better. In a globalized world, first world workers don't call the shots any more and the workers - the unions - need to realize that they aren't just competing against their own governments and the state next door. They're competing with globalized labour that can significantly undercut them and there are markets beyond first world borders that matter - and if unions come in all guns blazing, pulling a Detroit and demanding they get their way, they will be crushed by larger forces. The unions of today can't dictate - they need to play a game of give and take, and use their power to compromise from a position of weakness unlike they were in decades ago.
Unions are important, and one study won't change that. Unions must change with the times though and no politician, no unified movement no matter how large, is going to roll back the clocks on this one. Unions need to stay alive for what is to come, and unions - along with worker expectations - need to change too.