Chavo was a reliable performer, who could go in the ring. He was an experienced veteran, but at the same time, Chavo really wasn't a big loss. He wasn't going to be placed in the Intercontinental Championship picture, and he was never going to become a contender for the World Heavyweight Championship, because Chavo is not on that level. In the long run, Chavo's loss will be forgotten, because he is not one of those guys, who could make or break the WWE.
CM Punk on the other hand is a different story. Punk has proven himself as a top heel in WWE, and he is a unique villain. He's the squeaky clean straightedge superstar, who's covered in tattoos. He's the hardcore rebel, who isn't afraid to speak his mind. Punk can deliver some fine matches, and his mic skills are very impressive. Punk is the total package, and his loss could hurt WWE in the long run.
Shawn Michaels has entered the full retirement phase. Sure, he might pop up and make a special appearance on Raw every now and then, but his time in the ring is done. The Undertaker is banged up, and old age isn't helping. I think Taker will be used on a VERY limited basis from now on. He could return for some of WWE's bigger pay per views (Summerslam, Survivor Series, Royal Rumble) and we will surely see him at Wrestlemania, because streak matches have become a main attraction at the big show. I also have similar feelings about Triple H. The Game seems to be taking a backseat in WWE, and he isn't one of the main guys anymore. Also, Edge might have been plagued by injuries, but his second face run was pretty successful, and Edge was one of the more popular veterans in WWE.
As far as dealing with WWE BS goes, I don't think this is something everyone is going to avoid, unfortunately. Pro wrestling is a cutthroat business, and backstage politics will never go away. Also, I think a lot of wrestlers aspire to join the WWE. The WWE is the big leagues, and a lot of wrestlers will want to give their dream job a try.
As far as popular veterans go, Rey Mysterio, Kane, and Big Show are still around, but Mysterio really is the only one, who comes to having the star power that HHH, HBK, and Taker do. WWE is losing a lot of their big name veterans. Retirements, injuries, and reduced roles will continue to be a problem, and there's nothing anyone can do to stop this.
I don't think WWE is on the brink of a crisis, and I do think everything will be fine. Some people might hate John Cena, but he ALWAYS manages to draw a passionate reaction from live crowds. Some fans love him, and some fans hate him, but everyone is always anxious to see what John Cena will do. Randy Orton's popularity has exploded over the past year. He receives strong reactions from live crowds, and he has been crowned as the leader of the blue brand.
Smackdown has a strong mid card, and WWE is trying to push some fresh talent on the Raw brand (Alex Riley, Alberto Del Rio). WWE's top two faces are holding both of their World Championships, and I think Cena and Orton will do a fine job with leading their respective brands.