No, I agree. Twitter as a general-purpose communication platform is impractical. Yet a ton of industry figures have crowded into it for some reason. Twitter is the flashy, arbitrarily constrained version of what fingering other people's .plan files was in the 80s and 90s.
The 140 char limit turns it into a new journalistic form - almost anyway.
I have many issues with it, in addition to the sign-in page and general lack of access:
For non-celebs, the value of having tens of thousands of followers is often close to zero, so it's more vanity nano-press than useful communication channel.
For newsy events, real-time reporting is incredibly noisy and repetitive.
Retweet count isn't a good reader value marker. There should be some better way to find the best content.
Developer relationships aren't great, and unlimited access to the firehose would help create some innovation - which is badly needed at this point.
Handling multiple accounts is painful. If you want to use the same devices to tweet for a business and tweet as a person it's really not fun.
Twitter management history is uninspiring. No one seems to be in charge of thinking of cool new stuff, so Twitter is turning into formerly cool old stuff.