1) True, when I said I am not familiar with voltage regulators, I only meant I have not designed or made them. My company is making such regulators in Europe and US. I had heard that in US these are popular instead of providing OLTC in step down transformers. But it is a costly proposition and in IEC world we never used them. In IEC world OLTC is provided on HV neutral of step down transformers while US prefer OLTC on MV side. But in IEC world we had a need for such regulators recently.( these are small auto-transformers with a simple OLTC for controlling input voltage by +- 10 %) When small distributed power generators (roof top solar and wind turbines) started feeding power to grid through distribution transformers, it became necessary to automatically control the input or output voltage of DTs ( these are usually provided with DETC for +-5 %) to feed power to grid. So in Europe a need arose to provide voltage regulators on MV or LV side of distribution transformers. From 2015 onwards ABB is marketing such voltage regulators- LV up to 250KVA and MV up to 8 MVA to fit near to existing DTs. In new DTS, OLTC is provided in transformer itself and MR has developed a new simple low cost model, vacuum type, for use in DTS.
2) In 1970s&80s,when we were facing acute power shortage in India, voltage dip at consumer end was a real problem. We used to make DTs with OLTC during those days for +_15 % voltage variation. Now no more we require them except in special situations as above.
3) There were separate IEC and IEEE standards for voltage regulators.In 2018 these were combined and issued as a common standard viz. IEC 60076-21/IEEE C57.15.But Maximum rating is limited to 1000 KVA single phase or 3 MVA three phase; max 33 kV. So I am not sure whether 20-30 MVA voltage regulators are normal as Mbrooke mentions.
4) Of course nothing is impossible. In India, some years back we used to make 100 MVA 100/110 kV auto-transformers with OLTC. In India, 100 kV transmission voltage came in 1910 at Mumbai.At that time it was the highest transmission voltage in the world. But later 110 or 132 KV became standard, so a need came to interconnect this 110 KV grid with old 100 KV lines and the need for such special auto-transformers.
5) Vacuum type OLTC came in to use more than 20 years back, first in US with reactor type OLTC. But it is replacing only the arcing contacts and all other parts remain the same. So it may reduce maintenance liability ( a great advantage where tap changing is frequent eg HV DC transformers, furnace transformers etc) but I am not sure of reliability improvement.