I have been trying to illustrate my posts with photos, but I have had no luck in finding a half decent picture of taiatari done correctly. This perhaps illustrates my point that we do not do enough of it.
Certainly in Europe, there is a reluctance to teach taiatari, as many instructors believe that it destroys correct form. Very often kirikaeshi and kakarigeiko are taught with the explanation that hands should just touch lightly in chudan after shomen and that kakarite should then move on to the next waza. In some ways this leads to a vicious cycle, where people do not do taiatari because they cannot do it correctly and they cannot do it correctly because they do not practice.
Certainly bad taiatari is to be avoided, particularly when the action is to push from the upper body at shoulder height, catching motodachi in the chest, or worse, the face, but taiatari is an essential part of Kendo. You often need to make taiatari to set up hikiwaza and to benefit from jogai hansoku in shiai.
I have practiced with a number of senior sensei, who regularly teach butsukarigeiko. At one dojo in Kansai, they make it a regular part of any training session.
I believe the secret to successful taiatari is not to compromise your posture. After hitting, keep your arms and shoulders relaxed, drop your hands into correct tsubazeriai, keep you balance between your feet and slightly drop your hips forward. This should be enough either to move your opponent, or at least to put you in safe, close distance ready to make your next move.