When Dungeon Masters know that players will have Inspiration more often they will take this into account when designing encounters. Therefore players will, logically, try to increase the percentage of time they have Inspiration to a higher percentage than the DM expected when designing the encounter. The DM will respond to this, if successful, by ratcheting up his expectations, and thus encounter difficulty, again.
Eventually you will end up with every player trying everything they can to always have Inspiration, to spend Inspiration frequently, and to regain it frequently.
Do you want a game in which players hunt Inspiration as if they were addicts looking for their next fix and willing to do anything to get it?