I don't think there's much denying that Int is too much of a dumpstat. It does have some useful skills tied to it, but they're all those type of skills where having one party member who's good at them helps everyone, and having multiple people be good at them is redundant and almost totally pointless. Moreover, Intelligence is actually really important to being successful at just about anything in real life, which makes its status as a dumpstat even more ludicrous. On the other hand, it's always been sort of a double edged sword because casters get so much from their main spellcasting stat that you don't want to give them a bunch of extra stuff on top of it, which is the main reason that Str, Dex, and Con are typically "better" than Int, Wis, and Cha. This is an example of how D&D's attribute system really isn't that great and should have been overhauled for 5e instead of clinging to useless sacred cows.
That said, I'm not terribly keen on using Initiative to balance it Int. While it's also arguable that Dex is a tad overpowered, this has the drawback of requiring modification to monster stat blocks and also just isn't terribly interesting. Also, Initiative isn't really about quick thinking (which isn't necessarily under the purview of Intelligence anyway), it's about agile reflexes (there really should be an agility attribute that is separate from Dexterity, but I digress).
So, what's my solution? A modification of the Hero Point system - Instead of getting a fixed number of hero points at every level, you get tactics points per day equal to 2+ your Int mod. These can be used to add d6 to any d20 die roll, just like Hero Points. Like HD, they only recover at a rate of 1/2 per day, so while you may have a maximum pool of 6 or 7 tactical points, you'd typically only get about 3-4 uses per day. The reason I like this is because it's so broadly applicable, as Intelligence actually is, without really encroaching on the role of any other attribute. As an example, this could be used for an Initiative roll to simulate agility of mind or situational awareness in helping combat reflexes.