The characters should have access to all their original abilities, weapons and sub systems. Especially now that the game has been out almost a year (!). There is no reason that Jonathan shouldn't have access to all his weapons, or Alucard his shield summons or familiars.
While everyone having all their abilities would be fun, it would cheapen and unbalance the experience even further. Maybe if those extra abilities were only usable in single player, but in multiplayer, it kind of adds insult to players that want to enjoy the Chapter longer instead of some lame speed run that's boosted with abilities they can exploit, which results in dumbing down the playthrough and therefore require less effort and less feeling of accomplishment.
Can you imagine Shanoa with all her Glyphs and Glyph Unions? Julius with Grand Cross? Alucard with Shield Rod + Alucard Shield? Even on Hard, bosses would be vaporized the instant they enter the room, especially when you multiply their best abilities times the number of players.

Okay well if they added a harder difficulty..... you're right more HP to bosses would just make the fights drag on. But their power in Hard isn't enough to add enough danger and demand more skill from players. You can beat any boss with minimum effort on Hard once you skill up/equip them with the best stuff. Having their entire arsenal from their past game(s) would be more than overkill.
And most people don't want to nerf their build to challenge themselves, they expect the game itself to place a bigger challenge on their lap. That's why a higher difficulty that punishes mistakes further would really take things to a new level and keep things difficult instead of the difficulty level evolving from Hard to 'Easy', and Normal to 'Very Easy'.
Since there are no fatal pitfalls like the classics, the spikes and traps should kill in one hit. And bosses should be able to kill anyone in less than 3 hits.
(well some of them on Hard can kill in 1 hit, but I think more boss HP could also help balance things further because the bosses having fatal attacks doesn't mean much if players can kill the boss in seconds anyway.)
But I strongly feel if they added everyone's abilities from their adventure, a Very Hard/Extreme difficulty would have to be added before that, to avoid the balance of difficulty from tipping over completely in favor of the heroes side, with the enemies side being even more pathetic pushovers.
I mean look at Chapter 3, people don't even bother using the swinging weapon to damage the boss anymore. They just shortcut and spam their ranged attacks. More abilities would simply lead to faster methods of killing it, and Chapters can already be cleared too quickly as they are.
Yes even now the characters are unbalanced but what's important about their abilities is that they already have enough in their arsenal and growth potential (Skill Level/Equips) to survive and defeat anything. So people who like using characters like Jonathan , Alucard, Yoko, etc. shouldn't be discouraged just because another character has more tools and advantages.