Most of my bikes are set up with 7 speeds on the freewheel / cassette. Nearly all of these have two-tooth differences over much of the freewheel or cassette, which allows good fine-tuning of power & cadence. Two-tooth jumps are a bit less suitable at higher speeds, where it means a bigger change in speed or cadence. Some of them go to 3-tooth differences in the larger cogs, but this is simply to keep the percentage difference similar (an ideal cassette or freewheel would have a logarithmic progression of cog sizes). I use 2 or 3 chainrings on these bikes (typically a 46/36/24 or 40/24) to achieve a wider overall range.
In this situation, the advantage of a 8 / 9 / 10 speed setup would be to extend this relatively small cog difference over a wider range. But an nx10 drivetrain may not have much of an advantage over a nx8 or nx9 if the added rear cogs aren't ones you use (or need) often.
BobbyG above describes a 7 speed with a huge jump between the largest & next-largest cog. Shimano markets this as "Megarange", with 6 decent jumps and then the ermagherddropdowntocrawlspeed "bailout" gear. I actually don't mind this on a bike used mostly on flatland & gentle grades, but might occasionally see a steep hill.
If moving to fewer in the rear, what I would recommend avoiding is situations where you end up with a 3-tooth jump early in the sequence such as the unfortunate 15-18 jump on several Shimano cassettes. That can leave you grinding or spinning when you'd rather be somewhere in between. Again, having more rear cogs can help with this, but verify, especially on wide-range cassettes.
Selection of chainring size can affect how happy one is with the rear gears. It used to be there were many options, but unfortunately most current systems lock you into a very few choices.
On my recumbent, I still have a 14-32 6-speed freewheel. But I use half-step gearing with a 3-tooth difference between the outer and middle chainrings so I can fine-tune my power & speed.
One one of my bikes, I'm running a 1x9 with a 11-36 in the rear for minimal weight and simplicity. I'm actually satisfied with most of the jumps, except sometimes the 11-13-15 is a little too much of a jump in between and I'm thinking that a 12 or a 14 might be useful. But not to the point where I'm giving up on the idea.