Let's get all of the facts straight here.
When you walk up to the car and it is asleep, it will respond relatively fast. Can you run to the car jump in and start driving on 3 seconds, I doubt it, but I don't remember ever having to really wait for the car. And it is as fast as ICE vehicles.
I just checked my car and from app start to information was only 20 seconds. If it is taking 2-3 minutes, that is indeed an indication that it may have a very weak cellular connection. If the open trunk command didn't work, that it a definite indication of cellular issues.
Can I get in within 3 seconds in my ICE cars? Yes.
Does the Model 3 take 3 seconds? Hell no. Assuming it recognizes my phone the first time and unlocks, getting into the seat is the same as the ICE. However, after hitting the brake (which you can do as you sit down in one motion to save time), it takes a couple of seconds to start up. As others have reported, if you pull the shift lever too fast, it won't shift into D or R, and you waste a couple of seconds waiting for it to do its thing, before you can try again.
That's assuming two major things go perfectly. Which they often don't for me.
It doesn't recognize my phone. Out of the 5 times I got into the car to drive today, it recognized the phone (iPhone 7+) once. Had to use the card the others. That was a pain, as the first couple of times, I sat outside stabbing at my phone for a couple of minutes trying to get it to work. Then wasted another few minutes inside the car messing with the phone/app. I eventually gave up and just used the card. Next couple of times I waited a few seconds, and just went straight to the card rather than fiddling with the app.
The other major assumption is that it starts up when it unlocks. It doesn't always. There have been several times where the car will unlock and I get in (with the phone), but it takes a good 20 seconds or so to wake up. Very annoying as it's super hot right now and I'm sitting in a really hot car with a black interior, waiting for the damn car to wake up and start the a/c. Eventually, I see the Tesla logo and everything turns on. But that wait is really annoying and it happens a decent amount of times.
Whether true keyless where I keep the fob in my pocket and hit the start button or unlock with the fob and stick the key in ignition, both my ICE cars are quicker and ALWAYS reliable in letting me get in and start everything up. We're actively looking for a single replacement for those two cars, but it's gonna be another ICE. I love the Tesla, but it's still incredibly buggy and isn't a total replacement for ICE yet. It still takes quite a bit of effort to do things an ICE car does reliably all the time with no extra effort (from unlocking and starting, to camping in the boonies).