What is the benefit of a pasta pot with an inset?

The pot at the top with the holes in the lid allows you to drain the pasta without a colander or second container, so you have one less thing to clean. In my experience it's sometimes hard to get the pasta fully drained with one of these depending on the pasta because the holes are too small.

The perforated inserts are somewhat similar, you can cook the pasta and then drain it by just lifting the insert out. You can prop the insert over the open pot to let it drain which will both allow the water to drain back into the pot and keep the pasta warm while it's drained.

Another big advantage is that you can cook several batches of pasta in a row with the same water. This is often how restaurants do it, you often don't need this at home unless you are cooking several different kinds of pasta for some reason. I do this sometimes if one person is gluten free and others are not, or if I am cooking 3 different kinds of ravioli that have different cooking times, or if I am not sure how much pasta I need like for a big party, and want to be able to make more quickly if needed.

You get the best results with most pastas using a lot of water, as much as 4-6 quarts (1.0 - 1.5 gallons, 4–6 litre) of water per pound (450 g) of pasta. The pasta is better able to expand and absorb water evenly and won't stick together. The larger pots with an insert provide an easy way to do this.

I find these gadgets inconvenient, so, I would say no real advantage. I cook pasta in a large stock pot, and remove with a spider to the pan with the condiments. I can even cook several batches in a row this way. I don't really find inserts helpful, and don't need the extra "stuff" in my cabinets. Your point about extra expense, space, and clean up is accurate. I will also add that the insert takes up significant volume in the pot, so you actually lose usable space. They are just not necessary. Spend your money on a good, solid, multi-purpose stock pot.

That kind of pasta pot has many uses in the kitchen. I use the pot by itself to cook stocks, process smaller batches of cans, make soups and chili, etc. Besides cooking pasta in the insert is very useful for steaming large vegetables or large quantities of vegetables - I used mine last week for steaming artichokes and today for corn.

Pasta-wise the insert is handy because it lets you cook more than one kind of pasta, and it also lets you keep the pasta water rather than pouring it out. Pasta water is very useful for thickening sauces as it is full of starch, I stick a ladle in once the pasta is done and use it as necessary. You can also dip the pasta back in and lift it out if the pasta starts to stick.

These things are all about production! When we need to get lots of pasta out fast and fresh and have limited stove space, we can't afford to throw perfectly good boiling water down the drain (it takes a lot of time and energy to boil water). As others have said, you can also just use a hand strainer to scoop out the pasta, but this is slower and occupies a person who could be doing something else.

All that said, at home, I just use a regular pot, like you.

If your pasta touches the bottom or sides, the temperature can get higher since the heat would be conducted directly to the pasta from the metal surface. Having the barrier prevents pasta from touching the sides and it should be cooked evenly at the temperature of the boiling water. You can also put water in the bottom and use it as a steamer.