I'm a beginner to Chinese so maybe I'm misled, but I find it quite silly that all books and tutorials describe the third tone as "falling-rising". This is something that left me scratching my head at the beginning of my learning because the descriptions in courses just didn't match what I was hearing.

From what I hear, it seems to just be a short low tone the majority of the time, as you describe in 我家. Then it becomes a second tone before a third tone, as books say. But I hardly ever hear it as a falling-rising tone. Practically only when it's pronounced in isolation (e.g. when one is counting). So I wonder why the least frequent case is presented as the rule and the most frequent case is often not presented at all... maybe tradition from old pronunciations of Chinese?

Are you opposed to using it as a learning device to help bootstrap? Or are you referring more to its long-term, continued use? Or its use at all?

Except that if you use a western keyboard you still need to learn Pinyin or Romaji in order to be able to type the language. In my own attempts to learn a little bit of Japanese I've noticed that it is indeed difficult to associate the 'new' characters to the correct sound without using Romaji as an intermediate representation but my hope is that the more I learn and interact with the language the less this is the case. I think that, especially when using online learning tools, learning Romaji is inevitable and don't think that learning the phonetic system 'from scratch' makes it easier (if it is even possible to completely forget about your own phonetic/alphabetic system).

In short, as a starting learner of Japanese I acknowledge that the problem you describe exists but think that 'really bad' is an overstatement and it is almost inevitable that your brain associates your old knowledge of English (or other languages) to the new language.

I learned Chinese in Taiwan with Zhuyin, as a child. The first thing the teachers got was instruction in Zhuyin, and the way our books and teachers taught Zhuyin was by giving latin characters and English words with corresponding letters. Just looking at Zhuyin did not tell my English-trained brain I was learning new sounds from scratch.

In college I was taught Pinyin and we were given instruction on the correct pronunciation of each phonetic sound, positioning of the tongue etc., and the teacher spent time drilling us on that.

What matters is good instruction. Using Romanization doesn't encourage more correct pronunciation. Roman and Cyrillic alphabets are used for all manner of languages with completely different phonologies.