Music was meant to communicate, to reach its audience and achieve its composers intention, whether that be pure entertainment, some emotional effect, some intellectual stimulation or whatever. I think Striggio and Tallis had different goals for their music than, say, Sullivan or Raff. I have heard recordings of their music that affect me, so I'd have to say these recordings were successful.
It's the communication that matters, not HIP or modern instruments. If the performances were to be recreations operas would probably appeal to me much more, so I avoid productions where the stage director has been too 'creative'. I have been to very Spartan productions that really worked: student performances of Verdi, Poulenc and Rossini, village productions of Gilbert and Sullivan, a Don Giovanni in the Estates Theatre, Prague; and to a very grand one that also worked: Turandot at the Met with Eva Marton. La Boheme on Broadway was also a success, for me. I have been to productions that failed completely, for me. (Rhinegold at ENO a few years ago.)
Shakespeare at the Globe also works, even all-male casting, because the words come through- if the actors know how to deliver them. At that level they mostly do. A production of 'The Birds' in Greek would not work for me, because I do not understand spoken ancient Greek.
In this group the only thing we all have in common, I suppose, is that we listen to recorded classical music. Tastes clearly differ. Some conductors are anathema in some music to some of us, others see them in a very different light. I have been affected by Beethoven's 7th symphony in recordings by numerous conductors (Coates, Weingartner, Toscanini, Mengelberg, Stokowski, Klemperer, Boult . . .) so there is no single way to make the music live for me. I have been bored to death (or at least stopping the record) by others who I won't name. (I may yet see/hear what they were doing, so I try again from time to time.)
A Greek observed that you can never stick your hand in the same river twice- but he was incomplete- you are never twice the same you when you do, water flows, experience changes us.