It's more about the theme, not the game balance
Incantations and arcane words are the common fairy trope in many cultures. This is the main reason why verbal spells exist in D&D. Possible tactical applications are the consequence, not the reason of their existence.
The game evolved around fantasy tropes (spellcasting included) and archetypes, incorporating them into lore and mechanics. If you remove them, this naturally changes the game balance — there are features like Subtle Spell Metamagic which were designed specifically for circumventing such kind of limitations.
All these things are very situational, but they still matter:
- Silence spell is supposed to negate most of the spells (the majority is verbal-based)
- The verbal component is the "perceivable circumstance" you can react with Counterspell
- Underwater spellcasting can be difficult (apparently, this is not the case, but worth mentioning)
However, you don't want to change the rules by removing verbal components. You just want to introduce a magic item, which allows its user to speak aloud (presumably via telepathic activation).
So I have a question for you. How is it supposed to change the story? Let's say your character has "The Collar of Speaking", a magic item that allows a mute wearer to speak. As the result, the character speaks normally by using the collar instead of his mouth. Does this really change anything?
This character can speak. The way he does it not so important, it is just a fancy fluff like Kenku curse, or a personal characteristic like "I want my voice back" bond. Both are allowed by the game without any rule-bending.
Regarding the "speak through a familiar" idea, you should elaborate it first. The Find Familiar spell itself has a verbal component. Moreover, a familiar is an independent creature. You can't just speak "through" it, unless a specific game feature allows it:
Voice of the Chain Master
while perceiving through your familiar’s senses, you can also speak through your familiar in your own voice