I thought the STE's increased palette was pointless even at the time- it still had the same 16 colour onscreen limit (in regular use) as my STFM, which was always the main limiting factor by far. So why bother? (IIRC even the ST magazines themselves thought this.)
Pretty sure that if anyone had been offered the choice, they'd much rather have had 32+ colours even from 512, rather than 16 from 4096. (Yes, I know the former would likely have been harder, which probably explains why Atari went for the easy "enhancement").
I've no doubt if you wanted to create true 16-level greyscale images in Neochrome it might have offered a minor improvement- as well as marginally smoother gradients on games and possible other niche uses- but in general it appears to have been a "looks nice on paper until you think about it, useless in practice" improvement.
Of course a bigger palette would have been better, but 4096 colors did make some difference. Especially if you were into Spectrum 512 style images. The pictures photochrome could do with the STe's palette were stunning for the time. But even many games could use programing techniques to put more than 16 colors on the screen.
Really the STe's main features were the DSP sound/hardware scrolling/blitter. Games that actually used these things no long felt laggy with sub-par sound as many ST action games felt. Unfortunately not enough games took advantage