Mercedes: Negative affinity is an overrated drawback. It really isn't an issue getting anyone to C rank.
Holy Knight seems more like an offensive Faith magic class or a lance user with some utility than a support class. Mercedes seems best as just a bishop as movement isn't really an issue given her physic range and all of the movement abilities and you can get her +1 move from riding if you really want to. Ashe: I had a lot of success with ashe once he became a sniper. The massive range of bows made gave me so much flexibility in how I could engage any situation. I eventually made him a bow wyvern which really stunted his original role with less general offensive ability, but equally more flexibility. Ingrid: Kinda just felt like a worse bow knight. There was rarely a situation where her mobility trumped a bow knight's range and her low survivability made her very niche.
I haven't seen the heavy weapon balance in this game. There just aren't a bunch of OP heavy weapons that are so much better than the lighter ones. Sure she doubles anyone, but that rarely does more than someone with a little less speed and a little more strength.
I've also never had any problems with rushing. Sending your tanky dimitri, dedue, Sylvain (Leone for me) gave me more than enough time to make any objective a non issue. If anything Ingrid has less ability, because once she gets there, she can't really do anything by herself. She was very useful for sniping ballistas and other turrets with stride and canto, however.