Right near the end of the TT era before CD's took over the Japanese made some very nice high end LT tables. I have several, a Technics SL-M3, a Yamaha PX-3 and a Pioneer PL-L1000. My favorite is the Technics SL-M3. Super specs for wow and flutter and it's really cool to watch the arm tracking in operation. It's true that the arm has to go off center a tiny amount before the drive pulls it back in line again. There is a feed motion on the arm about once per revolution so since the grooves are about 0.003 to 0.004 of an inch apart it is never more that that far from being perpendicular from the groove. I don't think anything tracks that close and since the arm pivots it never loads the cantilever. Think about that, the stylus moves 0.003 of an inch towards the center and the tone arm is driven towards the center by a like amount.
These units were very expensive in the day and CDP were taking the world by storm. The three units above were the last hurrah by the Japanese before giving up on TT manufacturing. Find one of these units and have it serviced for years of trouble free operation.
There is nothing inherently wrong with LT TT, they were just introduced to late in the game. Technically they are much better that a swinging tone arm that spends most of it's time way out of alignment.