We all agree that using the "relativistic mass" as source of gravity is wrong... totally wrong in the theoretical sense. But it was not clear to me that it's wrong in the sense that it makes computation results worse than a purely Newtonian computation.
There is a slippery slope into uglier and uglier physics along that line:
1) Use relativist mass as source of gravity (thanks to me)
2) Use Lorentz transforms to correct distances, densities and times (see av8n)
3) Correct Newtonian computations with a finite speed gravity (search the web). The gravitational wave concept is a source of encouragements in that direction.
4) ...
But the temptations are so so strong:
1) Textbooks (introductory, SR and GR), in my experience, fail to warn against this.
2) Semi-classical quantum mechanics computations (while wrong in the sense of a consistent theory) seem to be useful; by analogy trying to do semi-classic computations in relativity is natural.
3) GR is complex, GR computations for actual experiments are scary and the relation to measurements not easy...