The high res modes of the 87V and the BM869s are definitely usable (but it depends, more on that later). Perhaps most of the negativity revolves around the marketing decisions, especially for the Brymen. When I received mine I know I was put off by the limitations, but they could have just been more clear and I wouldn't have been so annoyed. For the Fluke I think they should have flipped it around and made it a 20k count DMM all the time but made the 6k count mode be a "fast" mode.
I'd say all DMMs are going to do a fair amount of calculations/statistical analysis from the ADC output, but it's hard to fake too much and get away with it. If you only have a 14-bit ADC, then when you store the calibration point I don't see a way to get usable 20-bit values later, no matter how you massage the data. They have one single ADC making x-bit numbers, and that is what is used to store the calibration data. (Interestingly, the Fluke 8558A/8588A does have dual ADCs, one 28-bit for high accuracy/resolution at 8.5 digits and one 18-bit for speed at 6.5 digits.) So if 50% of your values are 1.0000V and 50% are 1.0001V, then it's reasonable to consider the actual value to be 1.00005V. But this requires the samples themselves to be quite good.
Based on my experiences with the 87V and BM869s, both can easily do the job so I don't think they are relying too much on math to save them, although it's obvious there is some amount of filtering/oversampling.
For the BM869s I've found the accuracy greatly suffers if you're very far off from the calibration temperature. I last calibrated mine at 73F and at 63F it's about 80 counts low in 500k count mode.