I did a few more DIY-kits and used thinner solder and concentrated on using less of it and the results do look better and more of that "slightly concave"
The reason for the concave filets is that a bad joint that is overfilled might look kinda sorta like a good one. But if you have a good enough view of what you're doing/seeing as you do it (with good lighting and magnification if necessary, this is pretty moot, IME. You can watch how the joint fills and know it's fine, then overfill it all you want, no problem.
It you are making one single joint out of the blue and can't see what you're doing until after you set your iron down and take a macro picture, then yeah, you might accidentally mistake an overfilled bad joint for a good one.
Or when you are going along and one joint takes longer before it wets out, this could be due to thermal coupling to a plane or a large component... this is where you have to take more notice of not accidentally making a cold joint.
It's basically a rule for your workers. Do as I say, not as I do, because I don't trust any of you monkeys. So if you are applying for a job as a production solderer, then yeah, be a good boy and practice your concave filets.
That said, when you do let a cold joint get by, it can waste quite a bit of your time to debug, and it might not be today. It might be 3-4 years later when it causes a problem.