Tail surface anti-icing is absent from a lot of jet airplanes.
The L1011 is but one example.
Even the B707...it came from the factory with tail surface anti-icing installed, but it was disconnected by many 707 operators, with regulatory authority approval.
The primary reason that tail anti-icing is missing from many large jets (and some smaller ones) is that during certification flight testing, either with flights behind a spray aircraft, or with various shapped blocks glued to the tail surfaces, no adverse flight difficulties were found.