[RPG] If you cast a cantrip as a bonus action, can you also cast a cantrip as your action

This house rule really only changes two not particularly powerful spells and is unlikely to unbalance anything

This house rule would only change anything when the character casts a bonus action cantrip spell. Searching on donjon I can only find two such spells, shillelagh and magic stone. Both spells give the caster a weapon to use so without spending the casters action to use it they aren't getting much out of the spell. Based on how limited the spells affected are I don't believe this change would unbalance anything or even come up that often.

Quickening doesn't change anything since the cost to quicken a non-cantrip spell is the same

As @MrNattious pointed out the cost to quicken a non-cantrip spell is the same as the cost to quicken a cantrip. Under the normal rule you could cast any full-action cantrip and whatever quickened spell (be it cantrip or non-cantrip) you wanted along side it. With this house rule you could quicken the full-action cantrip and cast the other spell a a full-action to get the same result. There is no change.

It would appear that Crawford's weighs in on the cantrip rule is only with relation to spells that are cast with the bonus action, this also made it into the Sage Advice Compendium.

Crawford confirms here.

Question: Can I misty step (bonus), fire bolt (action) and fireball (surge) on same turn? Or need action surge also be a cantrip?

Crawford: In that situation, the Action Surge spell would also need to be a cantrip

Crawford: The rule on bonus action spells pertains to your whole turn, not to a particular action (PH, 202).

PHB p202 Under Casting Times and Bonus Action

You can’t cast another spell during the same turn, except for a cantrip with a casting time of 1 action.

Since Action Surge gives you a whole other action and not a another turn you can certainly cast another spell so long as you did not use a Bonus action spell.

The Sage Advice Compendium also provides clarification:

If you cast a spell, such as healing word, with a bonus action, you can cast another spell with your action, but that other spell must be a cantrip. Keep in mind that this particular limit is specific to spells that use a bonus action. For instance, if you cast a second spell using Action Surge, you aren’t limited to casting a cantrip with it.