Anyway, I just subscribed.
When I went to grad school for a Master's at an engineering school which, at the time, was small enough to not actually have formal departments, I studied a fair bit of mechanical engineering but actually did a materials science thesis.
So, if you have the capability, certainly go both... It will give you, at your age, the ability to build the change you want to see in the world....
Tldr; it's a lot of coursework but I've never regretted it.
I'm a TPM now, have worked on aerospace projects with small teams where it helps to be fluent in both sides of the electronics and mechanical design. I've managed multi disciplinary design optimization efforts where there is heavy intersection between code and real-world mechanical factors (writing code for my mechanical designs and writing the backbone for other contributors or translating their system to code). Being able to understand electric motor systems design end to end through the entire chain from control comms to firmware to MOSFETs, electromagnetics, and mechanics has been rewarding for me as well.
In terms of opening opportunities, small hardware startups are where I've been able to have impact, and where there is demand for someone who wants to contribute in both areas. Where I am now as TPM is a fairly limited track and PM is a bad word in some companies. At faang, it seems that software track pays better than tpm or mechanical so that is one item to note.
At larger companies it is a difficult sell for someone who wants to do both at the same time as an IC. Smaller niche companies are more likely to want someone who has the breadth and can help fill in gaps or own a whole project.
The reason I am not a pure SWE is that my passion lies in being able to hold the result in my hands at the end of the day (or week, month, year:)
I'd recommend you try out the machine shop or what is available to you if you go to an engineering college, maybe some robotics projects, mechanical engineering foundation courses, material science courses. See how you like it. I'm sure you will be successful whatever you do. If you do both it's a lot of work but I never regretted it for a second.
You could just take some of those extra earnings and take up MechE as a hobby.
Maybe if you are a MechE working for facebook or twitter. But go to something like SpaceX or BMW and you will find the best MechEs paid way more than the software people. The insane paychecks in CS only exist at companies where software is the final product. Companies that produce physical products put CS into a support role. A department head at Boeing or LM is far more likely to be from an engineering background.
For the record, I have an ME undergrad (and a grad degree that's basically material science) and while I've mostly only used my direct classwork a bit, I've done fine.
And the idea that basically any other engineering major will make 20% of an even remotely typical CS major is idiocy.