I don't think so. Instrument Guidance System (IGS) or LDA (Localizer Type Directional Aids) in the US only allow for non-straight approaches. Kai Tak Airport in Hong Kong used to use IGS due to mountains blocking the way for a standard straight approach. Chep Lap Kok replaced it and it no longer needed IGS.
I have yet to come across an airport which accepts ICAO Category D or above aircraft and doesn't have at least Cat I ILS.
Smaller airports with only VOR/DME would often be only large enough for general aviation, or Category B or C aircraft. Major European airports have adopted ILS and other precision approaches as standard, and part of that is due to how commonplace Autoland is.>>1155482
Non-precision approaches are very uncommon in commercial aviation. ICAO Category D and E aircraft never use airports which don't have at least Cat I ILS (unless it's an emergency). Category C aircraft (such as the Airbus A320 and Boeing B737) do go to VOR/DME equiped airports from time to time, though this is usually if the airport has its own limitations (being remote, being barely used, or being a former military airbase which doesn't have ILS but had a military equivalent).
Some airports in Asia or Aerodromes in some parts of the word have no approach systems and will require an approach under VFR.