Just a couple of points, more specific to the B737. The use of ATM after anticing/de-icing or during LVOs is company specific.
The use of the ATM would also be prohibited when an engine power guage is u/s (EPR or N1).
Kuobin the wheel rotation is stopped before/during gear retraction by the brake system and whether the anti-skid is operational or not should have no bearing on the matter. The reason that the use of the ATM is prohibited without anti-skid is the greater stopping distance required. The use of full power should mean you arrive at your V1 speed sooner, which translates into less distance travelled down the runway, which in turn gives you more runway to stop on if you abort the take-off.
Inop. anti-skid has possibly the largest effect on the B737's performance, depending on the model you are talking about, reducing your take-off weight by about 8000Kgs, and it also has the single greatest effect on landing performance too.
Apologies for aircraft type creep!