6 wheel holonomic drive feasibility

[T^2]

Let's break down your response.

Thanks for your reply. The reason we're trying to push with a mecanum drivetrain is that "not having enough traction and power" is the only argument anyone on my team has made against getting mecanum wheels (and they're saying it a lot).

The "traction and power" issue has largely been addressed already in this thread. To sum up, traction in the forward and reverse direction is not significantly weaker on mecanums compared to standard wheels, and forward/reverse power is reliant only on the motors and gearboxes. In the sideways direction, of course, mecanums lose out in both. (There are many threads explaining why this is.)

If there's a way to have both in addition to holonomic steering, there would be no reason not to get the wheels (besides price and assembly and possibility that it won't help at all and whatnot)

You're completely wrong. Not only are there significant mechanical downsides (weight, size, complexity, number of gearboxes required) to mecanum, but they also come with a huge opportunity cost. The time and money you waste on those things could be much better spent training your students to make a drivetrain that works, and what's left over can be spent on the rest of your robot.