It's nice to dream about but as a concept it's inherently flawed. Unless you put very specific restrictions in place, it's just going to devolve into a contest of who has the safest and most punishing early game laning power in a vacuum.
The answer is cait. It's always been cait, every time this mode has come back. If not cait specifically because of bans or draft or whatever, people will pick the next best thing which will be another adc. Adc's auto win 1v1 lanes in a vacuum against non adc's, and in a contest of adc whoever has the strongest lane phase wins.
If they made a mode where you picked one of the roles (marksman, fighter, mage, assassin) and then it was always a duel between the same roles, or even if they just matched it up so everyone was in a mirror match, that would at least bring the mode closer to the idea of skillful 1v1s between mains of various champions like you imagine when you think '1v1 map'.
Otherwise it's just going to be cait or whoever is closest to her in laning strength all day.