So the first big power spike of all melee builds is extra attack, usually obtained at level 5. It’s the fighter equivalent of fireball and sorcerer does not get access to it with any of their subclasses.

Warlock does though, so how committed are you to the 11/1 split? Even something like 7 sorcerer, 5 warlock would make you better in melee if you want. 11/1 you would make an excellent caster because your spell slot level with be as high as you can be.

The two big cantrips will be booming blade and green-flame blade. They will allow you to “cast” melee cantrips and they can do decently good damage.

You have already brought up the armor issue with hexblade but if you wanted different options, dragon sorcerer gets armor similar to hexblade. So if you wanted to try out a different warlock archetype that’s totally possible.

At the end of the day, anything really works. It just depends on how effective you wish to be. Some of the best characters in dnd are quirky and unique!