Normally, the rules are very strict in that you only ever get one bonus action. If you were to convert that bonus action to an action, then there would be instances (Action Surge, Haste, etc.) that would then allow you to do this more than once.
The specific impact will be variable based on the specific bonus action under consideration, but changing it to a mechanic that would enable more than one could be very problematic.
I will review several interactions below that highlight the problem. The spellcasting actions are most problematic not because of being able to cast more than one spell (or not), but because many spells utilize the bonus action mechanic to control the spell. If you can use that mechanic twice, you are doubling the output of every spell that has that control mechanism.
Ready Action and Bonus Actions
Typically, you can not use a Bonus Action in a Ready Action. If you can convert your Bonus Action to Action, then it potentially works with this mechanic as well – giving further flexibility in how you use it and allowing for greater use/misuse of the secondary damage dealing that I cover later in this answer.
Bonus Action control mechanics and Bardic Inspiration* are two things that would benefit immensely from this
For instance, a Bard could now be able to hand out two Bardic Inspiration dice in one round. This doubles their current limit of one die.
Being able to hand out multiple instances of this limited resource could sway an encounter by boosting your party’s effectiveness at twice the speed.
Spiritual Weapon/Heat Metal (or any other bonus action damage/attack mechanic)
Giving more than one Bonus Action here will allow multiple instances of damage delivery from these spells. If upcast, you could be looking at a max of 5d8+Modifier for spiritual weapon or 9d8 for Heat Metal. Any spell that allows a delivery of damage via bonus action would benefit and would become significantly overpowered as it doubles the damage output over the length of the spell (generally 10 rounds.) Especially if you compare that against other 9th level spells like Meteor Swarm. (Big Thanks to Axoren for this inclusion!)
To be clear, this is not casting the same spell twice, or overlapping effects. It is using the bonus action control aspect of these spells twice.
The damage output of spells that use bonus actions to damage would increase
In direct comparison, let’s look at the damage outputs (assuming failed saves and successful attacks) for some of these to highlight the power of allowing two bonus actions to deliver damage from an ongoing spell/effect.
Meteor Storm as our Control example
Meteor Storm is one of the most powerful damage dealing spells available. I’m going to use the damage output from this as my measuring stick to compare against the effects of a dual bonus action mechanic.
Meteor Storm is an AOE, so it could effect as many creatures as you can fit within it, but each one would get a total of 40d6 damage. That’s an average damage of 140 per creature in the range.
Spiritual Weapon is a single attack spell, but lasts for 1 minute with an average damage of 27.5 (assuming +5 modifier) being delivered twice for 55 damage per turn for a 550 total over duration. In order for Meteor Swarm to be outperform this, you’d need to get 3 targets which may be difficult to achieve.
Bigby’s Hand provides another OP option. In this case, the hand is much more versatile. It can be used via a bonus action to act as a controller (interposing itself between two creatures or shoving them) and as damage (Clenched Fist/grasping). Utilizing the single hand to have two potential targets alone is very powerful. If we look at the damage dealing for Clenched Fist, we have a delivery of 108 damage per turn or 1,080 over the duration. Meteor Storm would need to target 8 creatures in it’s area in order to have a similar output.
Heat Metal is only effective against someone wearing armor, but in this case it would deliver 81 fire damage per turn guaranteed. Meteor Swarm would have to target more than 10 to become equivalent.
Dual Bonus Actions are very powerful
While you may get 5+ targets in a Meteor Swarm attack, it’s highly unlikely that they’d be arrayed in such a way and one of the most powerful spells in the book becomes dwarfed by many other options.
But the real kicker is you are now spending a minute dealing massive amounts of damage with only a single resource having been spent (especially for things that don’t involve concentration where there is no risk of not completing the full minute.) The economy of doing that is overpowered.
Not only all of the above, but the one class ability where you could start to challenge the need for this is with the Potent Spellcasting. This class feature is a method for increasing the DPR of that specific class. If you do allow two bonus actions, thjen it completely negates the increase that Potent Spellcasting provides and greatly minimizes that level 8 class ability.
*Although Bardic Inspiration uses a limited resource, it shows that it removes limits on other features as well.