Since we're talking most accomplished, that's talking achievements. Not peak level, not consistency, just the titles under the belt.
In terms of consistency, there's an argument for Ferrer, but his peak was below the Big 4 so he didn't win many other tournaments, but made plenty SFs and Fs. Berdych is similar to Ferrer, just a little more peaky. Still behind Zverev in achievements.
Off the top of my head:
Rios has him tied for M1000 equivalents. Rios did hit #1, but did not reach as many GS SFs and won 1 fewer ATP Finals, plus no Gold Medal. I'd say Zverev ahead.
Davydenko has no slam finals, less ATP Finals, fewer M1000s, no medal.
Tsonga has similar slam achievements, but no ATP Finals, no medals, and 3 fewer M1000s.
Nalbandian has similar slam achievements, 1 ATP Final, no medals, 3 fewer M1000s.
No one with no slams has more ATP Finals, so there's that. Same with gold medals. The ways people can be ahead of him are more slam finals and more M1000 equivalents.
More slam finals: Steve Denton, Kevin Curren, Miloslav Mecir, Cedric Pioline, Todd Martin, Alex Corretja, Mark Philippoussis.
More M1000s: Can't be bothered. I'm going to go on a limb and say anyone with
just more M1000s and fewer gold medals, ATP Finals, and slam achievements will be worse.
Denton looks like he took advantage of a weak AO field. Never got even close to another slam. Don't know about other tournaments, but unlikely.
Curren has 1 more slam final, but fewer semis, fewer ATP Finals, fewer gold medals, fewer tournament wins, fewer M1000s.
Pioline is better in slams, but has no ATP Finals, no medals, 1 M1000. Zverev ahead.
Martin is also better in slams, but no ATP Finals, no medals, no M1000s. Zverev ahead.
Corretja has another slam final, but 1 fewer ATP Finals, no medals, and 3 fewer M1000s. Zverev ahead.
Philippoussis has another slam final, but no ATP Finals, no medals, and 4 fewer M1000s. Zverev ahead.
Mecir has 1 more slam final, but 2 fewer ATP Finals, 2 fewer M1000s. I'd say Zverev ahead. Probably the closest?
Unless there's someone important I'm overlooking, yes. Zverev is the most accomplished player to not win a slam.
List:
- Zverev
- Rios
- Mecir
- Nalbandian
- Corretja