What are the consequences of not caring about traffic jams?

Solution 1:

As Dennis noted, service is a huge part of this - all the services in the game only work if transportation is available (of course, power uses power lines, water uses water pipes, so they aren't affected by road traffic).

This gets worse as the city grows bigger - it's very easy to have all your service trucks stuck in one traffic jam. Note that the service buildings don't have a finite range, the way it's indicated in the UI - that's just the range where they're effective. They will happily travel through the whole city, through three different traffic jams to get to a point where they are needed, and then back again. There is a limit to how long they can spend on a trip, but it's pretty long. Something that looks like a fun traffic jam in a 20k city will completely paralyze a 60k city. Seriously, I've had a city drop from 80k to 50k over a few weeks, just because of traffic jams!

Industry can only work if it has the resources. If you're seeing many abandoned buildings, this is one likely cause. This is much more important when you have e.g. wood industry without a forest - all the wood has to be imported. Industry creates huge traffic in the mid-late game.

And I've observed increased taxes after fixing traffic issues. I'm not sure about the cause, it might be that commercial zones produce more money when they get people-traffic. Or it might be the better service access, who knows.

And of course, traffic jams add a lot to noise. This can be countered (trees), but it's a factor.

Solution 2:

There could be issues such as garbage trucks not being very efficient. Likewise any service that uses the roads will have difficulties. Fire trucks, police cars etc.

With that information in mind I am sure you can make the decision whether it is worth it to you, to remedy the situation or not.

Edit: Additionally it creates some noise pollution, which will reduce nearby land values and the happiness of people.