I'd say that there's probably not nearly as much mobility in unit composition as there is in the modern US military. You don't have guys who are mechwarriors with the Davion Heavy Guards, who transfer to the 3rd Crucis Lancers, and then goes to do a stint with the Draconis March Militia for a couple years before doing a tour with the Fed Suns Armored Cavalry, then cross-training for a year with an artillery brigade, then taking a desk job for a couple years, then getting some LAM training, and finally finishing out your career with command of the second battalion of the Fifth Ceti Hussars.
That probably doesn't happen. Instead you probably join one unit, and stick with that unit. Half of that unit's mechs are probably owned by a Duke or a Marquis, and he's not gonna want people he trained (and who are loyal to him) to go off somewhere else and work for some other noble. So there's probably not as much upward mobility in terms of rank. You probably don't have a standard progression where you go up every few years. You probably have to wait for spots to open. Then you're more competent than the other people waiting for that spot. Either that, or you buy yourself a command.
So let's say that Junior von Nobody has finished the academy, is a 5/6 pilot, and has a tactics roll of 7+ on 2D6 (2nd ed Mechwarrior). Well, he's not all that great. If he wants to rise above Lieutenant, and lead more than a lance, then he's going to need to be better. He's going to have to wait until Captain Jones, leader of his mech company, isn't in charge anymore (death, capture, retirement, his own promotion, or whatever). And when that happens he needs to be the best candidate of all the lance commanders. Or his family can make a donation to ensure his promotion. If his daddy can swing a deal where another lance of mechs are made available to his son's unit, well than guess who the new Captain is?
This would probably be especially common in the Lyran Commonwealth. They have lots of social generals who just bought their way into command. The Fed Suns probably has more people who earn their position as far as command goes, but they've got problems of extremely powerful nobles who have their own virtually private armies.