So am I correct that if I have a new Mac with Mac OS and ARQ installed and if I restore the 3 folders: /Applications, /Library and /Users from an ARQ backup, it would be equivalent to restoring from a corresponding CCC backup (that is no need to re-install all the apps)? And ARQ is able to backup the /Applications, /Library and /Users folders without any problem as system disk utilities level copying is not required?
Yes, restoring all those folders will restore your apps and most (maybe all) license keys as well as your user data. But it will likely cause other issues as simple overwriting of system data (/Library) can be troublesome. Whilst this will allow you to avoid reinstallation of most apps, I would not describe it as equivalent to using CCC or Time Machine.
Try to use backup and recover apps to their strengths and not to try to bend them to other usage. My recommendation:
For complete recovery (all apps, licenses, user data) use Time Machine or one of the cloning apps (CCC, etc.) to a directly attached disk drive. These methods are designed to enable complete and fast recovery.
Use Arq (or similar) for backup to cloud (off-site) storage. Recovery only in disaster scenarios involving the loss/destruction of computers and local backup storage. I would not expect to do a system restore from Arq, but I would expect to recover all my data - documents, photos, etc. Remember that after your house has burnt down, having to buy or download new copies of apps would be a minor inconvenience.
Keep a record of all license keys in off-site storage. That can be digital (e.g. files backed up using Arq) or paper records at the bank or, more likely, a friend's house.
That is the way I use Time Machine and Arq.
If complete recovery (without any app reinstallation or entry of license keys) after a major disaster is a requirement then I would buy two or more disk drives, use CCC to clone, and keep at least one drive stored off-site. How frequently you backup and swap drives will be a decision for you.
PS. Safe storage of passwords can be just as important as licence keys. Increasingly apps are tied to subscriptions and are enabled by user/password - e.g. Dropbox, Adobe.