In the late 1990s/early 2000s laptop and cell phone manufacturers started phasing out Ni-MH batteries in favor of Li-Ion. The main reason for this seems to have been that Li-Ion cells do not suffer from memory effect¹, which is the major drawback of Ni-MH cells: if they are frequently charged without having been completely discharged, their capacity drops rapidly.
During the transition period, Li-Ion batteries were mostly reserved for high-end devices, or the costlier option where a device was available in either configuration.
The main obstacle to universal adoption of Li-Ion seems to have been the cell voltage of 3.2–3.6V—in contrast to the 1.2V of Ni-MH cells, which is in the neighborhood of alkaline batteries and led to wide availability of Ni-MH cells in the standard alkaline form factors, whereas no such ”household sizes” ever evolved for Li-Ion.
Today, when I look at the specs of robot vacuum cleaners, I see that most come with Ni-MH batteries. Ariete offers one single model with Li-Ion batteries, which seems to be their low-end model. Also, they have proprietary battery packs—so neither cost nor the standardized form factor seem to have influnced the design decision.
So why are Ni-MH batteries so common in robot vacuum cleaners?
¹ Edit, since there’s some confusion about the term: For the purpose of this question, “memory effect” shall refer to loss of capacity (reversible or not) caused by frequently recharging a battery without fully discharging it first. (If there’s a more accurate, somewhat widely accepted term for this characteristic in Ni-MH cells specifically, a hint will be appreciated.)