Combat pure sorcerer (5e Optimized Character Build)

This build revolves around the idea to create a low char pure sorcerer which can be used effectively for combat while retaining a lot of its utility. It will be covered until lv 10, but it can progress even further.
Starting race: Wood elf for its dex bonus, the increased mobility and especially for the weapon training (mainly shortsword&longbow).
Starting point buy (27 pt): 8 15 15 8 15 8.
In total it will have:

STR: 8
DEX: 17
CON: 15
INT: 8
WIS: 16
CHA: 8

Sorcerous origins: Draconic bloodline for the AC and the additional hit point (alternatively a shadow sorcerer could work too if you can use darkness extensively. In that case replace a spell with mage armor)

Spells:
Given the low cha the choice will be towards the spells which have no saving throw. The only exception will be fireball at 5 because... well... it's fireball!

Cantrips: Booming blade, choose 3 other cantrips with no saving throw
LV 1: sleep, magic missile
LV 2: sleep, magic missile, shield
LV 3: sleep, magic missile, shield, invisibility. (Note: if you can make use of chokepoints then Cloud of Daggers becomes a good option to deal damage)
LV 4: magic missile, shield, resist elements, invisibility, misty step
LV 5: shield, resist elements, invisibility, mirror image, misty step, fireball
LV 6: shield, resist elements, invisibility, mirror image, misty step, fireball, haste
LV 7: shield, resist elements, invisibility, mirror image, misty step, fireball, haste, polymorph
LV 8: shield, resist elements, invisibility, mirror image, misty step, fireball, haste, polymorph, dimension door/greater invisibility
LV 9: shield, resist elements, invisibility, mirror image, misty step, fireball, haste, polymorph, dimension door/greater invisibility, animate objects
LV 10: shield, resist elements, invisibility, mirror image, misty step, fireball, haste, polymorph, dimension door/greater invisibility, animate objects, (teleportation circle)

At lv 1 the sorcerer has 9 HP, 16 AC (21 once shield is available) and excellent saves for the most common attributes (WIS, CON and DEX). The damage is dealt with booming blade, for a total of 1d6+3(+1d8)
At lv 3 the metamagics being chosen should be Quickened Spell and Twinned Spell. The first will allow you to cast a spell and attack with Booming blade on the second turn, while the second will allow you to twin spells like haste, polymorph, or greater invisibility
At LV 4 the points should go to DEX and CON, raising the number of HP and bringing the AC to 17 (22 with shield).
At lv 5 the damage on the attack is 1d6+4+1d8(+2d8) with booming blade. Alternatively you can use haste on yourself to get a damage equal to 2d6+8
At lv 8 you should either increase your DEX to 20 or pick a feat (mobile, war caster, lucky are all good options)

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