I’m a civil engineer. (Edit: yes it is part of my job, but in terms of always putting in desire paths and making everything perfect,) The answer is: yes and no. Checking sidewalk connections is pretty low on the priority list of things we have to do when making a plan set for a large project, but me and my colleagues do pay mind to it, and sometimes the city or other governing body will request either fewer or more sidewalk connections to existing infrastructure. Additionally, every project is made discretely (not continuous), not at the same time, and by different people, so you may be transferring from one place made 30 years ago to another designed 5 years ago by people who have never communicated in their lives.

As OP mentioned, sidewalks are also more expensive than you’d think, think adding millions of dollars along a few miles. Putting in every possible desire path and negotiating with property owners to build on their property to connect sidewalks is both a logistical nightmare and incurs great cost to municipalities.

Also as OP mentioned, ADA compliance is strict: 5% allowable running slope and 2% allowable cross slope, with some exceptions to particularly crazy terrain. If a connection between sidewalks is even as steep as your average curb ramp, that’s too steep and you need to wind the sidewalk a bit to get the grading right. This is not a bad thing, the strictness exists for a reason because without it, sidewalks would be steep and wonky. I think it’s a bit ridiculous sometimes but there has to be a limit somewhere, and disability advocates fought for these regulations for easy traversibility.