Class role appears to be very important to you. It's not to me, and I suspect it's also not to @auburn2
. If I'm in a party that has a character that can occasionally make themselves nigh-unhittable, I'm going to leverage it by striving, on those occasions, to ensure that the enemy's only
valid target is that character. Whether that's by using terrain, hiding, full cover, social engineering, or simply putting the character far in front (supported from a distance by long-range characters) the nigh-unhittable character is a resource for me to leverage to engage the enemy while limiting their ability to fight back.
It doesn't matter to me if that character is a fighter or a wizard--what matters is their effective HP total (as modified by their AC and resistance to being critically hit) and their ability to survive other threats (like elemental damage and debuffs). A Bladesinger who is using their defensive capabilities happens to be pretty good at those categories. And if I don't think I'm going to be able to make the Bladesinger the only valid (or at least, most appealing) target in a particular encounter (e.g. wide-open space, highly mobile enemies), then I'll employ a different strategy instead, and use the Bladesinger in a different role.
Doors are a natural chokepoint, however, which are ideal for limiting the enemy's melee options. Sure, they might choose not to attack the Bladesinger if the Bladesinger can't be hit, but with the Bladesinger in front blocking the doorway the melee enemies can't hit anyone else either. Maybe the enemy opts to use less-effective ranged attacks against the other PCs (who have cover from the Bladesinger). If so, that's still better for the party than a melee brawl, especially with the example party where the PCs have dominant ranged capability.
So yes, I'm absolutely going to put the Bladesinger up front when blindly breaching a door of a enemy structure. Of the four available characters, they are the most survivable option, and I don't dare have the rest of the party be in AoE range of the point character. Sure, the Bladesinger is taking a huge risk, particularly if there are multiple enemy spellcaster behind the door, but against those spellcasters it would be even worse to have the whole party standing in a group by the door, ready to be taken out by AoE.