I envision much better UI support (even if it's also manually approachable "on foot"). The player would be presented in their LFG UI options with a 1v1 Format; it would have rewards that make it worthwhile compared to the rest of their game time; it has to be supported with special auras/effects/pickable items because some imbalances are brutal on 1v1 by default (it doesn't need perfect balance but having some specs being "immortal" is crippling to the format).
PS Talk of UI improvements reminds me of the mistake of having casual BGs being incentivized over rated BGs; all players should enter rated BGs by default because that'd make them start as "easy rated" anyway (since even the inexperienced would enter them (and the people who run premades would quickly jump rank anyway); have non-rated stuff as a hidden separate thing in the UI just for testing addons and goofing around (a need mainly for the highly rated).