Is anesthesiology still a good profession to get into?

Yes: It is a very rewarding profession. I can tell from my own experience as a anesthesiologist.

Of course : Anesthesiology requires broad understanding of medicine. Anesthesiologists are very educated and fun to have around. Anesthesia includes many sub specialties , which allows you to do procedures, take care of critically ill, treat pain, etc. Or manage your practice. Your happiness will be determined by how good you are as anesthesiologist.

Yes: There are still shortages of all physicians across the country in all specialities. The population is expanding, the baby boomers are getting sick. There will always be a need for anesthesiologists and all physicians. This is also a portable profession, much like engineering, should you wish to try your luck in a new country.