The water bottles we all use are the way they are because they have developed according to rider demand for the perfect bottle over most of a century. 24 oz. standard bottles are less than 10" tall, quite a bit less, which says you haven't even tried a standard bike bottle. Go to your LBS and get a couple. I particularly like Fox bottles because they have a gasket in the lid, not necessary but I think keeps then leakproof longer. I think they're ~$7.00, something like that. Get clear ones if that's what you want. I like them the best for the reason you give.
And learn to drink from your bottle while riding. It takes practice, so start practicing someplace where it's safe to make mistakes.
Standard bike bottles are perfect to take everywhere.
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