Hey Luca and everyone,
Thanks for your suggestions! I’ll try to respond as best as I can.
Like/up vote/down votes: We’ve been talking about this internally for a while now, so it’s definitely on our radar. We recognize the value of not only the peer recognition, but also the quality control as @raphaelgoulart points out, which is very important to us and our community.
Constraints on tab names: We agree with this. When Hooktheory was just getting started this didn’t come up very often, but now that the database is expanding, it’s clear that not supporting certain characters is becoming an issue.
"Missing" chords: This is an important yet tricky issue. Hooktheory tries to strike a balance of maintaining the simplicity of the user interface while at the same time allowing users to compose/analyze with a robust and often complex set of harmonic tools, which sometimes requires tradeoffs. From the beginning, it was always important point for us that we build a framework that prioritizes chord function. We could have designed HookPad to allow users to put in arbitrary chords (e.g., entering chords by chord name and quality) the way that most other music software does. However, by encouraging our community to think about chord progressions functionally, we hope to to answer questions like, “Why do these chords sound good together?” rather than, “How do I play this song on my guitar?”. We also want to show people that music theory isn’t quite as scary as it seems 
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When we were first designing the backend to Hooktheory, we supported “embellishments” that included ♭5, ♭9, #9, #11, etc. These were mainly designed to accommodate so-called alt. 7 chords, that come up from time to time. Here’s an early example from Sara Bareilles’s Bottle It Up:
We eventually took this away, because they cluttered up the interface and felt their function was too limited. That being said, I personally find a few omissions particularly inconvenient. Without augmented chords, classics like Blackbird, and Stairway to Heaven can’t be properly analyzed. And V11, (which is commonly shorthand for V11omit 3, omit 5) is surprisingly common in popular music, and so far we’ve had to use V7sus4 as a substitute.
We agree with many of the points that @HertzDevil has made. For the time being, we don’t plan on adding ninth chords, although this may change. We don’t plan on allowing users to explicitly specify the quality of a chord, as we feel this goes against the spirit of HookPad. And if we do introduce augmented chords and fully diminished 7ths, we’d like to do this within our framework. As @HertzDevil mentioned, one way to do this and still remain consistent is to introduce a harmonic minor mode. We’ve thought about this extensively in the past and if we do decide to implement this, we’ll have to consider all of the consequences (e.g., being consistent when modes switch).
As always, we welcome your feedback on this issue.
Modulations: So far, many key changes are represented by separate TheoryTabs. However, modulations are obviously an important musical device that are commonly used in popular music. We have certainly discussed this issue, so it’s on our radar, and we will definitely consider it for a future update.
Extending notes and chords across lines: We’ve also been talking about this internally, and will implement this as soon as we find an adequate solution :).
Again, thanks for your feedback!