If people think the situation in tennis is more complicated than goal mouth technology, we're clearly talking about a different subject. I'm talking about the technology that is used to check if the ball was over the line, and also the one that is used when a player queries it. Both have been found wanting. There's an article on wiki that covers some of it.
I also fail to see why it's seen as such an issue. It reall does play a very minor part in the outcome of competitions. There have only been a handful of times when they technology may have proved useful, and panel reviews showed that the refs were right most of those occasions, probably more accurate than Hawkeye.
Combining the two, it would be bringing in technology to leave us no better off than we are now, but with the risk of it's short comings being an excuse for other interference with the game for the benefit of tv.
As for what I would favour the resources being used on instead, I've already said it, a panel reviewing the game and heavily penalising simulation. My bet is it would take a matter of months, then this apparent spare resource can be used on other matters, such as standing or Policing. The odd doubtful goal decision is way, way down the list of priorities.