I wasn't even taking the Shield spell into account, since it's a much more limited resource than bladesong is. But it is a little different than an EK doing it since they're a 1/3 caster whereas you're a full caster minus a bit for the monk dip.
You can only (I think) have AC 21 at level 1 if you are a fighter who foregoes a bunch of damage potential to wear a shield and take defense style, and you somehow acquire plate mail, which costs 1500gp. Since the fighter has to give up damage to get that AC it seems fair to assume agile parry which has a similar opportunity cost. So compared to the fighter who is fully optimized for AC and has spent a whole bunch of gold on armor, the level 3 monk/bladesinger with your house rule using mage armor, bladesong and agile parry (all of which can be on pretty much permanently) has 13 + 3 + 3 + 2 + 2 = 23.
Thinking about typical level 3 encounters, in LMoP you're facing things like hobgoblins, who have a +3 attack bonus. So even without shield, they need a crit to hit you. Essentially your house rule has cut your chances of being hit by 2/3 (since RAW they would still need an 18, which is 3 in 20, which you've reduced to 1 in 20). Against a +4 attack bonus you're cutting hits against you by half; against +5, by 40%. That means that over the course of an adventuring day you can take about twice as many attacks before going down. That's a really significant impact of a house rule. Granted it's less of an impact at higher levels as attack bonuses go up, but maybe not by that much since you're a class that can raise their AC and their casting stat, or their AC and their attack stat, with the same ASI, and so you're continuing to go up in AC even as attack bonuses rise.