Reference the comments above about "why use a diamond".
You can indeed use a carbide tip, or even another abrasive to dress the wheel, but it's horses for courses. I use a coarse carborundum stick for roughing the wheel but it leaves a crushed grit surface with a limited abrasiveness – it blunts the wheel grains and therefore the wheel loses some of its free-cutting properties. A wheel surface which is blunted in this way will cut as if it were a finer grit, but will generate more heat as the grains rub rather than cut. A carbide tip will have the same blunting effect as it crushes the grains it touches exposed on the periphery of the wheel.
Different wheel materials give different results – I have a white wheel I use for sharpening twist drills etc (HSS) and this is less susceptible to the "crushed grains" effect. Understanding the different effects of this means getting into the intricacies of the wheel construction – a green grit wheel for example is a hard grit in a relatively soft bond so the grit is renewed quickly as it cuts. A grey wheel is a soft(ish) grit in a hard bond so it survives the rigours of daily sharpening HSS with occasional (whisper it quietly) contact with bits of mild steel.
A diamond cuts the grains, and as a result leaves a much more free cutting wheel surface. It will cut more freely and cooler, and behave as a wheel of the designated grit.
If you want a really free cutting wheel – particularly if it is a fairly coarse grit wheel for coarse material shaping – then the old fashioned star wheel dresser is the thing. This pulls grit particles out of the surface of the wheel, creating a horrendous abrasive dust hazard, but the advantage is that the wheel will cut with a vengeance.