No, there are not dangerous consequences
In playing since 2014, and DMing since a few years after (against my will at first) I have found that Inspiration does exactly what it is intended to do: now and again you can overcome a bad roll.
We have done it both of two ways.
Roll with advantage when you make an attempt, a saving throw or an attack. This works best with players who pay attention to detail so that they call out the advantage roll in advance. Any roll with advantage tends to have a decent result. (Usually, not always).
Roll again after a poor roll. This is far easier to implement.
If you fail a d20 roll you could've used Inspiration on, but before DM narrates the effects of this fail, you may spend inspiration to reroll. It doesn't count as advantage, and if you rolled with disadvantage you also reroll with disadvantage. You must use the new result.
That works a lot like point number 2. Your house rule is fine.
How often you award Inspiration becomes the bit that you control as a DM. If it is rewarded now and again, the math factor gets lost in the noise. If you award it a lot, which I have seen in play, it still does not have an overbearing result.
If each player has one Inspiration point at the beginning of each session (many groups I have played with have done this) we discovered that about half of them never get used because players forget to do it.
Option 3: I can pass my Inspiration to another player
From the DMG entry on Inspiration.
Players and Inspiration. Remember that a player with Inspiration can award it to another player. Some groups even like to treat
Inspiration as a group resource, deciding collectively when to spend
it on a roll. It’s best to let players award their Inspiration as they see fit, but feel free to talk to them about following certain guidelines, particularly if you’re trying to reinforce conventions of a certain genre.
We have found in the past six years that this is a great way to boost both teamwork and team morale. I strongly suggest that you adapt this convention. Both @V2Blast and @MikeQ (who are veterans of this site) are in my Saltmarsh campaign. We have adopted the DMG suggested option of passing Inspiration from one player to another, both in and out of combat.
It works.
It is a good idea.
Award Inspiration and use it.
My experience over just under 10 years is that your fears are groundless. The occasional reversal of a bad roll usually creates a boost of positive energy at the table on both sides of the screen.
Enjoy.