A tall thin pot is a hazard as it can be tipped over all too easily The book says use lots of water to ensure even cooking and to stop the pasta sticking.
But regular stirring will solve this problem too Just use less water in a regular pot and feed the pasta into the boiling water.
It takes about 30 seconds for long spaghetti to soften enough for it to fit into a regular pot.
It cooks just fine WITHOUT breaking it up if you give it a quick stir after a minute, and then every couple of minutes or so If you know your stove temperature and spaghetti type, it will only take a couple of goes to work out the least amount of water you can use.
I use about 1 l of boiling water for three adult servings of spaghetti in a medium domestic pot.
With the lid half on it is cooked to a firm bite point in less than 8 minutes, and the water just covers the spaghetti when finished
cooking.stackexchange.com/users/3203/TFD
Your suggested design would topple over very easily, especially on a gas hob with a grate, risking serious injury.
Aside from safety concerns, your design would also be inefficient as there is an extremely low surface area in contact with the hob.
It would therefore take longer to heat up.
Since the pasta is bunched together, there is a lower surface area of pasta in contact with the water, further slowing the cooking process.
Your design would also cause some serious sticking-
you'd likely end up with a stuck-together tube of spaghetti with this.
A smaller, normal-shaped pan can be used while avoiding sticking if you can be bothered to stir it more often, but a large pan with plenty of water would be the ideal solution.
cooking.stackexchange.com/users/6095/Mike
You need a lot of water to dilute the starch in the pasta.
Less water = more sticking.
cooking.stackexchange.com/users/4194/ElendilTheTall
If you use too little water when cooking your pasta (on the stove), the starch to water ratio will be too high.
This means your pasta won't "cook" or absorb the proper amount of water.
I purchased the "Fasta Pasta" as seen on tv "device".
It goes along with your question of a tall, thin pasta pot, but is made for cooking pasta in the microwave.
It uses a LOT LESS water than cooking on the stove.
I don't know why.
I seriously dislike "as seen on TV" gizmos, but this one was worth it.
cooking.stackexchange.com/users/5958/Macromika
The more amount of water in a pot the more consistant the water temperature will be.
A very small amount of water would cool down once the pasta was added which would take longer to boil, and cook the pasta at a lower temperature causing the center of the pasta to cook more which would likely keep the pasta from becoming al dente.
You could make fresh pasta if you'd like to have perfectly cooked pasta with less water consumption.
cooking.stackexchange.com/users/6135/evanlivingston
I've been cooking pasta (successfully) for nearly 40 years
and I'm here to tell you that you don't need a boiling pot of water to cook pasta to perfection.
You can start it in cold water and you don't need all the water that many espouse you need.
cooking.stackexchange.com/users/84502/Orland L Miller
If you really only want to cook one or two portions of pasta, you can also boil water in a wide, flat pan.
I'd say stainless steel is best - it shouldn't be too shallow - and cook the spaghetti in there.
Also works for other "long" foods like asparagus.
EDIT: I also think using less pasta water is better for getting starchier water to create sauces that then stick better, like pasta aglio e olio.
cooking.stackexchange.com/users/53980/John W.
Every time I cook spaghetti in a regular pot, I get the feeling that I could save litres of water if the pot had been created with spaghetti cooking in mind. This is especially true when I only need 1-2 portions. Cooking smaller pasta is more efficient.   Is there a culinary reason for using so much water? Do professional kitchens use a better method?
Why do we use so much water to cook spaghetti?
cooking.stackexchange.com
<equipment><spaghetti>
cooking.stackexchange.com/questions/14685
cooking.stackexchange.com/users/None/
Pasta needs a lot of water to balance out the starch, ensure even cooking and stop the pasta from sticking. A tall thin pot would topple over easily, have very little surface area in contact with the stove, allow the water to cool down when adding the noodles and not allow the pasta to cook al dente. You can use a smaller pot and feed in the noodles slowly or use a wide and shallow pot for fewer noodles if necessary. A tall, thin pot would fall over easily and the surface area in contact with the hob is very small. You need to have enough water to dilute the starch in the pasta.
It only takes about 30 seconds for the pasta to fit in the pot. The tall, thin pot would fall over very easily and a very low surface area in contact with the pot. You need enough water to be able to dilute the starch in the pasta.  You can also cook the pasta in a low, wide pot.