How game breaking would it be to allow a familiar to alter its form more quickly?

I was thinking about allowing the familiar to change form by entering its pocket space as an action, then being called out in its new form as another action. Since they are just spirits inhabiting the form of a mundane animal, altering their form does not seem to break anything I can see. Also, it would feel like the daemons from Philip Pullman's 'His Dark Materials'.

I was just thinking about them changing form as an action, but entering the pocket to reforge themselves feels more correct. I was also thinking that changing shape on a whim could have a combat mechanic that would be easily exploitable. This way the master and familiar both have to sacrifice actions to change the form. This would also mean that something like the chain would have the option to select their advanced familiar and it could adopt basic animal forms if it was needed.

It probably doesn’t change their in-combat power much.

It does improve their out of combat versatility a lot. The new familiar basically has all abilities of all possible familiars simultaneously, switching between forms at will. It has keen hearing, smell, sight, and blindsight; it can fly or climb or swim, including staying underwater indefinitely; shrink down to small size, be stealthy, or do mimicry. 

I think if you wanted to do this in-game it should still cost a spell slot each time you do it. The spell is balanced a bit around the idea that you get access to only one familiar form at a time for such a low level spell. Otherwise you can essentially swap casually between blindsight, dark vision, flight, swim, different stealth values, etc. But I think swapping out the hour casting time for a shorter casting time would be fair if the familiar is already summoned. I'd probably just make it a minute long... not long enough to seriously slow down the party, but long enough that it's not worth doing in combat. I would keep the component cost each time, though, so that would be the main cost of changing forms down the line.

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I would probably require the character to cast the spell again, but with a casting time of action. That way it isn't completely free, but also isn't necessarily tedious.

Alternatively, "Chimerical Familiar" could be a custom/homebrew feat, enhancing the Find Familiar spell (and requiring the character to possess it as a prerequisite).  Allowing the familiar to change its form freely and without material cost (i.e. no components, no spell slots) is very powerful for out-of-combat utility, but it's also a super cool Master of the Arcane sort of thing.  If a player is interested in this, they could potentially take the feat at a higher level, maybe limit the feat to eighth level or higher, and allow the character to choose whether to empower themselves via an ASI or a more traditional feat, or to use that chance for advancement to empower their familiar instead.  As a humongous sucker for Chain warlocks, I could very easily see myself investing in such a feat as both my companion spirit and myself gain in strength.

I like the feat idea, and it is a feat that be clever for in combat, but really is intended for out of combat versatility.

Chimerical Familiar Feat - Your familiar has the ability to alter its form at will. The shift takes an action and renders the familiar helpless until the beginning of its next turn. It does not immediately lose it grasp if holding onto something (a bat turning into a crow), or fall from the air (pigeon turning into a rat) until its next turn begins if the new form lacks the appendage necessary. The familiar is limited in shifting between the allowed animal forms unless it is an advanced familiar in which it has the ability to also take the one option selected.