Welcome to TalkBass!
I'm going to throw you a curveball.
1) I taught bass lessons for almost a decade. Most of my students were kids.
2) I sold music gear, especially pianos, for the same decade or so.
Human nature being what it is, go with the TC. Why? Gadgets. (They are fine rigs anyway.)
Now, the finger waggers will be along any minute to say "He shouldn't be playing with buttons and switches! He should be studying theory and doing scale exercises over, and over, and OVER AGAIN!" But let's get real. Kids are into technology. (My girls are 5 and 8 and they already teach their grandparents how to use a phone.)
While I was selling pianos, digital pianos made a huge leap in quality of sound, feel and buttons and whistles. At the time, all kinds of studies came out that showed kids who can practice with more interesting sounds will practice longer. If it comes with a headphone jack, that's a bonus. Even more studies show that kids who can practice with headphones practice longer and take more risks while practicing....in other words they "stretch" themselves more because they aren't afraid of making a mistake anyone else can hear.
Lifetime amp? Scratch that off of your list of considerations in my view. Since I began playing in clubs at 15 years old (46 years old tomorrow) my tastes in music gear have changed dozens of times. I have owned countless rigs. Your son will need to explore what HE likes when HE gains more context of what is and isn't important to him. So get him something he can use now and don't worry about how long it lasts in his musical career. He'll be fine getting something else a few years down the road.
You are one cool parent. My parents were very supportive of pretty much anything I wanted to try and that alone made me what I am today. Best of luck with it.
P.S. The Fender Rumble crowd are an enthusiastic bunch. You could ask what kind of garden hose to buy and they would stand up and yell "FENDER RUMBLE!!!"