Nice idea, but of course even spelling reform is near impossible, let along script reform—unless you’re Mustafa Kemal Atatürk and your country is post-Ottoman Turkey. And even when your language community adopts a script from scratch, practicality means the script will look a lot closer to the local majority or prestige language’s script. And the more IPA is not easily available, the more it will not be used.
Besides, historical orthographies have been argued to be a feature and not a bug.
The level of detail in the IPA would be an argument against practical use as a script, since writing systems need to be phonemic and not phonetic. In fact, the IPA was original intended to be used in less detailed mode as well as more detailed mode; the original proposal for example said that you could use <e> instead of <ɛ>, if your language didn’t have a contrast between the two. But that detail has been largely ignored.
The IPA would still need some tweaking to be used as a practical script, anyway. Or at least, the people behind the Africa Alphabet thought so…