Yeah, they are looking for the "freshest" ball to help the serve. Depending on the conditions of play, the balls can get fluffy rather fast. In damp conditions, they also absorb moisture, even more so when they end up rolling on the wet covers that are folded at the back of the court or land in the plants that surround some center courts, etc. In dry conditions, it has more to do with how coarse the surface is and if the ball got through a couple 40 shots rallies instead of a couple service winners... It would be interesting to try and make some statistics about it, but players often feel it is harder and harder to hold serve the longer a set of balls has been in play, so in interviews you see them mention how they were glad they managed to hold in the last game before the new balls or how they made a specific effort to try and take advantage of their opponent having to serve with old balls.
Though it really can't happen on the ATP tour, I hear some tricky players used to keep a fresh ball in their pocket so that several games later they could suddenly serve with an unexpectedly lively ball!
But checking the balls is also part of a routine. You have people like Wawrinka who checks the whole set of 6 (8?) balls every time, you have people like Gasquet who asks for the same ball if he played a good point, but you also have people like former player Davenport who asked for one ball and used that one. She probably decided that the benefit from picking the best ball was not worth the time it took and the distraction it caused.
What I always wondered and do not know, is if it could be beneficial to use a less lively ball for sliced serves. For a flat serve you want the fastest ball, for a kicked serve you want the one that will bounce the higher, but for a sliced serve you really want the one that will have the most curved flight, that will take the most effect and I am not sure how that works.
About the evolution of rackets and the impact it had on the game... it's a rather complex topic really. The materials of the rackets evolved (wood, aluminium, graphite, allowing greater and greater string tension), their shape evolved (greater head, greater sweet spot, more aerodynamic profiles), but the strings evolved also, like the infamous and promptly banned spaghetti strings and several generations of synthetic strings that "grip" the ball better and better.
[Side note: I hear in several federations, juniors are forbidden to use all synthetic strings and instead use half synthetic, half natural gut (like many pro do, including Federer), because the rigidity of the synthetic strings is traumatic for the joints, while the more elastic gut is much more comfortable.]
Obviously, this evolution allows for greater and greater control while maintaining power (my understanding is that a massive wooden racket with pure natural gut strings at a low tension is still the most powerful thing in tennis, providing you hit the small sweet spot and don't really care where the ball is going!). But as the rackets evolved, so did the players, getting more and more athletic, with guys like Borgs, ready to run down every ball for ever (which he did with a wooden racket) or Lendl, credited for being the first true modern professional in tennis as he was the first to do things like work on his diet with a dietitian, etc. Note that as players are getting more and more athletic, they also get taller and taller, because we know now how to turn a 6'5" guys into someone who can run fast and be stable on low balls (see Berdych's quads for reference!). But as the rackets and the athleticism of the players evolved, so did the surfaces. The grass of Wimbledon was heavily tinkered with to be slower and, to my knowledge, not a single event on tour is still played on cement or carpet. And the balls also evolved but that really is mess (I once tried to figure out which tournament used which ball, as players are always complaining about them, and I gave up pretty fast). Most notably, the balls used at Wimbledon used to be slightly smaller and I think it is no longer the case (they also used to be white, but now all balls are fluorescent yellow for increased visibility - during play and on TV).
So really, it feels to me the racket is only one of the many components at play. As they evolve for more spin / more control / more controlled power, they make it easier to hit passing shots, to stay in rallies while under pressure and to hit big ground strokes to safe targets. They also help with the serve (and Federer said as much when he went for his new racket with a bigger head / bigger sweet spot), but probably not as much as the increased athleticism of taller players. Afraid of Ivanisevic and his ilk, all surfaces got slower to reduce the dominance of the big servers, but as a result, there are only three guys left in the Top 100 that are pure serve & volley attackers...
Personally, I am rooting for a greater diversity in the speed of surfaces, because a really fun part of tennis is seeing many players with different play styles and see how those match up in different conditions. If all tournaments are played on slow courts, that will hurt the range of viable play styles.