Traditionally, adc/support go bot to contest dragon, and mid kinda fills in the gaps in the team with a relatively flexible pick - no hard requirements but a resilient champion with wave clear and either teamfight or roam potential is ideal.
Reasons you would want the mage mid and adc/support bot:
* Shortest lane helps more fragile, shorter range mages avoid ganks without escapes
* Waveclear helps establish priority and roam to help other lanes or assist jungle
* Bluebuff access
* I think bot tower is still weaker? And adc/support have the strongest early tower siege
Things that might mitigate the above or otherwise support swapping the traditional layout:
* Adcs and supports have and are expected to have much more wave clear than they used to
* Having "bot lane" mid makes it easier for top to roam to them and the mage (or assassin) is still able to easily roam to them. Only top loses gank pressure, which...no offense top laners, who cares?
* Adc+support mid makes early 4 or even 5-man ganks super easy and ridiculously lucrative - if your mage and top laners get priority you can just collapse mid and bust open the tower super early. Firstid tower down just shifts map pressure so damn much
*Dragon access is identical, and adc/support can probably support herald too for even easier tower blasting.
* You might end up with lopsided matchups if the other team doesn't match your "swap". In theory that would be equal on both sides, in practice you'd have the advantage of picking and playing with knowledge of your strat.