PIE laryngeals?

tgpedersen and sanctex-thank you for responses. However, my
question can be rephrased as follows. If the posited laryngeals
were deleted separately in each IE language, that appears to me
to nullify the basis for reconstruction. Assuming it doesn't
because of some data I am ignorant of, according to basic
reconstruction method, one needs cognate forms demonstrating
these consonants (their undetermined phonetic nature poses an entirely
separate problem which weakens reconstruction possibilities),
plausible sound changes in several languages and/or morphophonemic
alternations resulting therefrom (residue), etc.
If anyone bothers to answer these points, where is the opposition
to laryngeals (authors, bibliography)?