I think Tomy doesn’t recommend them, they also recommend against using nicads/niMH.
Big problem is that the charging circuit relies on the internal resistance of alkalines to restrict the current going into the BCG. Rechargeables and lithiums have lower resistance, so are able to pump through more current which might overcharge your car.
Lithiums when fresh also have a higher voltage… approx 1.7-1.8V vs drycell 1.5V and nicads 1.2V.
Aren’t red Energizers still selling for A$10/pr? They usually last only 3X as long as normal Energizers… but they cost 5X as much.