Is TSA lock compulsory for travel to US?

No, using a "TSA lock" is not compulsory. What using one does is enable TSA to physically inspect your luggage, if they so deem it necessary, without cutting your existing lock(s).

If you use a "TSA lock", it has been designed to allow TSA to use a master key to open it. Of course, this also means, as you have surmised, that anyone else with a master key can also open it.

If the locks on your luggage are not designed with a master key, available to TSA, then when you get your luggage at the destination, you may discover your locks have been cut off, or the combination lock has been pried open.

I would add that no lock has ever been designed, from the biggest to the smallest, that a determined thief cannot break, eventually. If you're worried about loss, that is what insurance is for. If you're carrying something truly irreplaceable, well... I don't know what to say as to why you checked it in anyway...

TSA locks are not "mandatory", in the sense that it's perfectly legal & allowed to bring any old suitcase with any old lock into the US. However, if you use a lock that is not TSA compatible, the TSA reserves the right to break it open if they need to check the contents of your bag.

The "other places" you describe seem to be more about Customs issues, where they're worried you're smuggling eg. drugs and can thus intercept you and your bag on arrival. However, TSA is concerned about security, so they need to screen bags before they get on the plane. They can't realistically do this with you present, not least because this would tip off if you were indeed a nefarious terrorist, so they need to be able to open your bags. And, of course, every country in the world scans checked bags and reserves the right to break into them or even blow them up if needed, lock or no lock.

Overall, TSA locks are a classic case of security theater: let's implement a back door only available to the "good guys" (TSA), and pretend it doesn't help the "bad guys" (thieves). In practice, of course, while distributing TSA keys to the public is supposed to be illegal, they're still easy enough to find online and a TSA lock will thus only defeat an incompetent thief.

TSA locks are one step above a rope as far as baggage security is concerned. I have locks on some bags, on all bags I use a coloured cable tie to secure the zipper. They cost 2 cents each at any electronics store and come in enough variety that no baggage thief will have another just like it. The seal is photographed at the check-in counter.

A plastic seal of course provides no actual security, it does provide tamper notice. I never pack anything worth stealing on checked baggage, and what I do pack is arranged in a way that looks good on baggage screening. Thus, security has no interest in my bag's contents and thieves tend to go for more expensive-looking (and not tamper-sealed) cases.

No, using a TSA lock is not mandatory. First, it is not mandatory to use a lock at all. Second, you can use any lock you want but, if the TSA decide to open your bag, they'll just break your lock if it's not one they can open with their master key. Note that they accept no liability for damage to your lock or your bag caused by them forcing a non-TSA lock.

No, using a "TSA lock" is not compulsory. That is because there is no U.S. law that mandates the use of such locks. On the contrary, there are situations in which the use of "TSA locks" are actually a violation of the law (49CFR 1540.111), even when a lock is explicitly required by law.

The primary example of when NOT to use "TSA locks", is when transporting firearms. Basically, the hard-sided container of the firearm must be locked, and "...only the passenger retains the key or combination."

So, since the TSA retains keys to "TSA locks", the use of such locks is an explicit violation of the law.

References:

https://www.law.cornell.edu/cfr/text/49/1540.111

http://www.gpo.gov/fdsys/pkg/CFR-2014-title49-vol9/pdf/CFR-2014-title49-vol9-sec1540-111.pdf