it was luck(plot armor), team work, Coil, the villains underestimating the undersiders,(possible Ziz plot and maybe PTV), and tactics. Plus the Alexandria was luck more than you think(tho it doesn't make sense why she need to breath when in stasis body, or how she ended up brain dead when her mind is basically being shunted to the shard). Did you know Alexandria and Taylor weren't even the same room when it happened They were separate by walls of concrete and people, Alex could have made the choice of just plowing through all those people and kill them in order to snap Taylor's neck and it wouldn't had take more than a few seconds, but that didn't happen so Alex instead did the opposite and try to go the opposite direction and get out of Taylor range and avoid casualties, because of that decision Alex die, instead of Taylor(tho it was doubtful Alex would have aim to kill Taylor). Taylor basically took advantage of the circumstances, in any other situation 9/10 Alex would have won any encounter with Taylor. About the S9 come on you're serious on that one Jack was playing around most of the time and didn't care if members got killed if he had it would have been a different story, heck I wouldn't call that even a win Jack cause Golden Morning still that was a failure, how's that a victoryRead Worm again sometime... it wasn't possible for Taylor to do anything against Alexandria or the Nine either, yet somehow she (ruthlessly and with escalation!) managed to pull thru anyway...
And About the undersiders getting involved, they maybe can now since Lung, Oni lee and March got dealt with. so now is possible to deal with Bakuda but then again do seriously think that insane women will go down easily, they will need people that can counter her Bombs and in canon it was Clock and vista.