Well you could, except, you can’t. How’s that for a straight answer?
There was a time when nearly every phone came with an antenna connector or an external antenna, or both. You may remember the odd little gold-plated hole on the back of a cell phone you had about fifteen years ago. It may have been hidden behind a rubber bumper. Odds are you didn’t know what it was used for. It was used, way back when, as a connection point for an external antenna. It was possible at that time to get external antennas, and for a short while some cell booster makers allowed you to wire the output from a booster through that connector. It certainly made a big difference to the connection ability of those phones, even if it did make it harder to carry the phone around with you.
And then… the iPhone happened. Actually it’s not fair to solely blame the iPhone for this, but it’s also fair to say that the iPhone really changed the way people thought of mobile communications. In the early 2000s, many phones were still pretty large, nearly the size of a soda can. They were thick, too. There was plenty of room for extra connectors, even if they were rarely used. By 2007, though, everyone wanted a thin phone, as thin as possible. Sure, the definition of “thin” has changed a lot since then, but the point is that the race was on to make phones that were as thin as possible. Even today as phones actually get bigger due to increasing screen sizes, they’re still getting thinner and lighter.
Most phones today are about 50-60% battery. Battery technology hasn’t kept pace with the rest of the world in terms of miniaturization and as we demand more and more power from a phone, those batteries actually need to get bigger. This means that space is at a real premium on phones, and it’s why so much money goes into engineering every tiny component to save as much space as possible. There just isn’t room for something people aren’t going to use, and let’s face it, people just weren’t using that external antenna connector. Getting rid of it allowed for just a little more battery to be put into the phone, which is something that everyone uses. That’s pretty simple.
There may be a few phones out there with external antenna connectors… I’ll be honest in saying that I haven’t seen every phone that’s currently sold in the whole world. What I can say is that it’s been a long time since I’ve seen a cell booster designed for direct connection, and since the 2014 FCC rules mandate that boosters be sold in complete kits, I can say that there is no kit designed for this purpose. It may be possible with enough knowledge of basic electronics, enough parts and enough time to cobble together something that could work, but you’d probably be invalidating the warranties on everything you touch there. That makes it your risk, and that’s fine, but as for me I find that a regular cell booster works very well and doesn’t require me to be wired to anything.