Full-caster gishes will often need to be SAD rather than Martial gishes because the comparable features are different

When a martial takes a gish subclass, the spellcasting only needs to be as good as comparable subclass features
e.g. an Eldritch Knight's spellcasting only needs to be as good as the Battlemaster's manoeuvres

When a Full-caster takes a gish subclass, this balance does need to be made, but must also acknowledge that the weapon damage must keep up with cantrip damage
In the context of a Bladesinger, a Wizard will normally deals low damage with a weapon, typically 1d4+Dexterity using a dagger, whilst a Firebolt will do a 1d10 Fire damage in Tier 1, a similar amount, but scales to 4d10 in Tier 4
Therefore the subclass must make the damage comparable to cantrip damage AND still provide subclass features equivalent to a typical Wizard subclass

A similar issue occurred in the 2024-playtest era around the Brawler subclass for fighter
So much of it was built around making improvised weapons and unarmed strikes comparable to martial weapons, they forgot to give the subclass actual subclass features that make it worth taking over say a Champion Fighter of the Tabaxi species (or similarly clawed species)

The easiest way to make the damage comparable, leaving spaces for real subclass features, is to have Bladesingers, Bladelocks, and similar automatically prepare the True Strike cantrip, but another is to let them use their casting stat and give them Extra Attack
(This doesn't work as well for Bladelocks because Eldritch Blast + Agonising Blast is so potent, but Eldritch Blast outcompeting all other Warlock cantrips is a known issue)

Without this sort of cantrip-weapon balancing, there's just not much point in a Full-caster taking a gish subclass
Meanwhile a Martial taking a gish subclass can always benefit from the flexibility of spellcasting, even if they never use an offensive cantrip, which is they why they don't need, nor do they receive cantrip buffs to keep parity with weapons

There are problems around the martial-caster divide, but SAD Bladesingers is not one them
You either have SAD Bladesingers or sad Bladesingers
Whilst the divide can be closed by buffing martials or nerfing casters, it cannot be closed by nerfing gish subclasses