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Recently, I've read Hennie's Paper. I understood the construction of buffer zones, but why can't it be applied to yield a single-taped Turing machine?

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Just because that UTM itself requires $2$ tapes to do its task that efficient. Removing one tape, the magic is gone.

But assuming you have the fantasy power to do efficient $1$-tape simulation, what gains do we have then?

That should be the question rather than your question.

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  • $\begingroup$ If an efficient 1-tape simulation is possible, then the problem of verifying palindromes can be done in O(nlogn) time, which is impossible, right? $\endgroup$
    – user93928
    Commented Sep 30, 2018 at 5:28
  • $\begingroup$ Then, computer science has more insights into many other computational problems. $\endgroup$ Commented Sep 30, 2018 at 11:36
  • $\begingroup$ But can we resolve the P vs NP problem assuming it? $\endgroup$
    – user93928
    Commented Sep 30, 2018 at 12:12

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