These are interesting points. Let's tackle them one by one.
Simplicity
The three basic Attributes need to be at least 1 each - it's written in the rules. One Attribute at 5 and two others at 1 cost 28 points already. Maxed out Determination and Impulse are 20 each. No points remain for Specialties.
But let's ignore the non-basic Attributes and use their 40 points to buy 8 Specialties. This gives you an awesome base of +6 for the appropriate Attribute, which you can also use for conflicts of other Types. If you are able to provide an appropriate explanation. There are many situations when Inappropriate Attributes are simply not appliable.
Likewise, you say a min-maxer could simply make their specialties as broad as the GM lets them get away with. This assumes the same thing as above - that the Game Master is soft and will let you screw him over. The GM should know when to say no, such as when creating characters in MnM, a system which is really easy to break.
Still, I should probably increase the cost of Specialties. Attribute cost could scale rather than be constant, too.
Determination and Impulse seem like good buys, and that's what they should be - they really let a character achieve more than just their skills normally allow. But that power comes at a price.
Genericness:
Don't think of 300 soldiers as 300 individual Conflicts. Think of it as a large Conflict (or perhaps a Challenge would be more appropriate here) with a high Difficulty. It's like in Risus, where rather than facing a lot of Orcs, you face a Horde of Orcs which is really good at being a Horde of Orcs (so its cliche is high).
That being said, how high would I grade such a large group of soldiers as an opponent? Depends on the setting. Anything realistic, especially if the characters are out in the open and have no support? Yeah, good luck with that. But if they are a part of an army and have to survive, then it would be a Difficulty ~8 challenge with Resilience appropriate to the number of phases of the battle (think of it in a dramatic way rather than actual strategy): something like 3-4. Likewise if the players are superpowered and face normal soldiers.
I'm not familiar with Break Blade, but by Shirou, Reimu and Shinji you mean the characters of Fate/Stay Night, Touhou and Evangelion respectively, right?
They are nowhere near the same characters. Not just in this game, but in general.
Shirou would definitely have a lot of Determination. His other Attributes would be low.
Shinji, on the other hand, has a lot of Impulse, with Determination steadily increasing as plot advances. It's the Eva unit going berserk as much as he does, though.
Reimu has high Attributes in general. Sure, she didn't work hard for them - but she still does. A Touhou setting would use different than default Attributes, obviously.