Well, how about the fact that our
devices do use rechargeable
batteries and not the one-time use & toss ones?

I also use those newfangled light bulbs, too.
Yes, but I'm pretty sure secondary cells are less recyclable than primary cells. They're not like lead acid that are virtually all recyclable.
One has to wonder how many of those folks making a stink about cigarette butts drive electric cars
AFAIK NiMH are common in electric drive cars, except the Tesla which uses Panasonic 18650s.
Here's Tesla's press pulp publication
Based on this info we can see 60% recovery is good for Panasonic 18650s (2200mAh & 3100mAh). It's at best a secondary source, but it's the best I can find presently.
The general opinion is electric cars are a net win even if the source power is coal, taking delivery and 70% charge Eff into account. The cited eff on the Tesla is 17.7 kW·h/100 mi Gasoline at 36.6 kWh/US gal presuming 40mpg would represent 91.5kWh/100 mi.
It's expected that the battery life is 7yr/100,000mi.
So 17,700kWh(battery) vs 91,500kWh (2500gal)
Coal = 40% eff, Delivery 7% eff, charge Eff, >95%.
33,391kWh(coal source) vs 91,500kWh (2500gal)
[6,150kWh/ton] [907,184.74g/ton] [gasoline 2914.45g/gal]
4925kg of Coal vs 7286.125kg gasoline
Add 6800 Panasonic 18650s with a mass of 450kg, with 40% waste with recycling, so add 180kg solid waste for battery pack.
So 4925kg coal, 180kg slag waste from
batteries per 100,000 miles, vs 7286.125kg of gasoline shot into the atmosphere per 100,000 miles @ 40mpg.