No, Subtle Spell doesn't remove/affect conditions (but it can help you cast a spell to get away)
The sorcerer's Subtle Spell metamagic option says:
When you cast a spell, you can spend 1 sorcery point to cast it without any somatic or verbal components.
That's all it does. It doesn't say that it removes or affects any conditions that your character has - and things do what they say they do.
So, for instance, if you used Subtle Spell to remove the verbal and somatic components of fire bolt (which are its only two components), other characters wouldn't be able to detect your spell until it was already cast. However, the attack roll would still be made at disadvantage. The same is true of shocking grasp.
The purpose of Subtle Spell is not to remove or affect conditions such as Restrained or Grappled; it's to make it impossible to detect that you are casting the spell (if it only has verbal/somatic components) until you have already finished casting it. This makes it impossible to counterspell the spell (if it only has V/S components).
In addition, it often lets you cast spells outside of combat without others being able to tell that you're casting a spell. This can obviously be beneficial when being seen casting a spell might be interpreted as a potentially hostile action.
For instance, you might want to cast dominate person on someone - but it's essentially limited to combat use because other enemies will see that you cast the spell just before the person starts asking weird. With Subtle Spell, though, there's nothing making it obvious that you're casting a spell, so it gives the spell more utility use.
Another example: you might want to cast a spell like fog cloud that obscures the battlefield and causes problems for enemies, but if you cast it normally, it'll be obvious to anyone who can see you that you're creating the cloud since it appears right after you speak the verbal component and gesture the somatic component. If you use Subtle Spell, however, the cloud of fog seems to just appear without anyone making any obvious gestures - making it less likely that someone who wants the spell to go away will focus their attacks on you.
Subtle Spell does what it says it does. It doesn't make it any easier to make an attack itself while restrained; it just gets rid of the verbal and somatic components of a spell.
(Note that things mentioned in the spell description text, such as the actual suggestion when casting suggestion, are distinct from the verbal component itself. The same applies to spells like fireball that describe some visible effect originating from your pointing finger to the target of the spell; they're not the same as the somatic component of the spell.)
Important note: Even if Subtle Spell doesn't remove the effects of the Restrained condition, it can help you escape whatever's restraining you. Normally, a caster might keep you from casting misty step to teleport away by casting silence to prevent you from speaking verbal components of spells. However, by using Subtle Spell, you can cast misty step without any components, making it much harder to stop you from casting a spell to get away.