The value of "learning to program" is roughly comparable to the 1st year of CS classes at a reputable University. It is certainly not a replacement for the entire degree.
Yes. IMHO this is what most often gets overlooked when people debate university CS/SE as a mostly-theoretical discipline as distinct from practical experience in industry.
You can study practical skills in using a certain language or library or tool, and you can become somewhat productive. But without sufficient theoretical understanding, you're just doing cookie cutter coding, and you will always have a relatively low glass ceiling on how much you can achieve.
Put more bluntly, practical skills are what you pick up to get from incompetent newbie to vaguely useful programmer in the first year or two on the job, but improving your theoretical understanding is what gets you from there to seriously useful senior developer a few years after that when you're no longer just writing simple GUI logic in C# or trivial ORM code for a Ruby on Rails web site back end.
Also, the degree is no replacement for practical experience.
Indeed, but someone with good theoretical understanding will pick up any given tool based on that theory fairly quickly.
Now, at no point in this post did I imply that getting a degree is either necessary or sufficient to achieve a good understanding of the theory. As far as I'm concerned, you absolutely can get there with time, effort and an open mind.
However, I think even autodidacts will find the process significantly easier if they've developed rigorous mathematical thinking and the ability to read and digest technical writing first one way or another. Also, for better or worse, the reality is that having that degree certificate will probably get you better jobs early in your career, which in turn will give you better experience and better colleagues to learn from at work.
In any case, just reading lots of casually written tutorial blog posts by people who've been playing with a tool for six months longer than you have certainly won't get you to that level of understanding alone. It's very easy to spend a lot of time doing that in a field like software development, feel like you've learned a lot and can be super-productive, and never even know how much you're missing if you've never found the right course of study or mentor or on-line learning resource to open your eyes. That, IMHO, is the biggest risk for people who haven't studied formal CS/SE one way or another, and sadly you can always find plenty of examples in the on-line forums for whatever the latest shiny technology is (currently I'd say it's front-end web development).