As IchoTolot said, 160px is the "standard" simply because that's what Lemmings 1 used. Since no convincing argument has been made for changing it, that's remained the default.
NeoLemmix has supported vertical sizes larger than 160px for almost as long as it's existed - Holiday Lemmings Plus, which was the second made-for-NeoLemmix pack ever released, contains a vertical scrolling level. Vertical sizes
smaller than that is a more recent feature but even that's been in there for a couple of years now - IIRC V1.47 was the first to support it, but I might be wrong here.
After setting it to 184 level covered 16:9 screen nicely.
What size will fully cover the screen depends to some extent on the exact resolution, not just the ratio. On many (but not all) resolutions, the choice of compact vs full skill panel can also affect this. Also - if we're not running the game fullscreen, then this would instead be based on the window size.
A 384 x 184 level will fill the screen exactly on a 1920x1080 resolution while using the full-size skill panel. But if you switch to the compact skill panel, there'll be slight vertical scrolling. If you switch to a 1280x720 screen, there'll be scrolling in both directions with either skill panel; and 1600x900 would have horizontal scrolling regardless of panel, with vertical scrolling on the compact panel and some vertical unused space on the full-size panel.
The only advice that can really be offered here is "you cannot fill the screen exactly for all users". If you really hate border area, you'll need to ensure all your levels are big enough to require scrolling on any reasonable screen resolution. The smallest level size that achieves this, if I've calculated (and come up with an accurate "list of common resolutions") correctly, is 428x230. We can drop this down to 428x200 if we only take landscape 16:9 displays into account; the 230 high comes from a 4:3 resolution (and if we restrict to 16:9 but allow portrait resolutions, the requirement is 428x208).
And even this is assuming default NeoLemmix settings (aside from perhaps changing between the two skill panels; I
did account for that). If a user, for example, has their zoom settings set to always be 1x zoom, while using a 4K screen (which is a very impractical setup, to be fair), your level would need to be 3840x2120 to fill the entire screen without border area - which I believe is more than the editor even allows you to make, although NeoLemmix itself has no problem accepting a level of such a size provided you've got plenty of RAM, and a CPU with very high single-core performance (as NeoLemmix does not make use of threads, apart from a separate thread for audio; and does not make use of the GPU either).