The reasons I don't like long coding assessment projects and the reasons I don't already have an example code profile are the same. Reinventing all the same wheels in different programming languages just isn't as fun for me as it once was, and I don't have as much time to dick around with any specific side project, especially ones that don't have any immediate utility to me or my family.
Does anyone ever ask about how I spec'd, designed, built, installed, and maintained my DIY entertainment center? No. Same methodology as building software, you know, except the problems are solved with different tools from a different toolbox.
If you're truly really looking for someone "T-shaped", you have to realize that the tittle on that T might include things entirely outside the realm of software or computer hardware, like how to hang a bear bag when camping, or how to fly a small single-engine aircraft, or how to train cats to use regular toilets, or how to run for political office, or what to do when you get a flat tire, or how to hold someone else's baby, or how to hit a gong target from 300m, or how to make a longbow for under $10 at Home Depot, or how to report a pothole so the city will fix it, or how to repair a pothole when the city won't do it, or how to play "Flight of the Bumblebee" while slowly rotating your B-flat concert tuba through 360 degrees.
All those miscellaneous, general-purpose skills do, in fact, make someone more effective at quite a lot of software-related tasks, sometimes in unexpected ways. But they are never going to appear on a resume, or crop up in the answers to any of the stock interview questions. When you include a criterion that specifically selects for people whose after-work hobbies also involve software, you are implicitly selecting against those who do other things, because there is much, much more to life than writing code.
There was only a very narrow slice of time when I actually wrote code for fun in my free time, from the ages of 15-25. It basically stopped after I got laid off from my first software job, and interviewing for software jobs became my next full time job. That's when I realized that I needed to do other things in my life, because it didn't matter how much I loved software if it didn't love me back.
So if you think need a portfolio to get a job, you might want to build one up that includes more than just code samples. The software industry does not love you back. It will move on to someone younger when it gets bored of you.