Speaking strictly about the US; don't know about other countries. Remember, when we talk about various fields such as physics, engineering (even specific branches of engineering such as civil, mechanical, or electrical), or medicine, these fields encompass a wide range of functions and tasks. Certain functions and tasks require specific certifications or licenses (which in turn may require specific degrees). Other functions and tasks don't. And even the functions and tasks that require specific certifications or licenses can in certain circumstances be largely performed by individuals without the specific certifications or licenses if the work is supervised by, reviewed by, and signed off by someone who does hold the specific certifications or licenses.
Let's suppose a physicist is someone who holds only degrees in physics; no other degrees; no other certifications or licenses. Then consider the following examples.
(a) Medical.
(1) Can a physicist treat patients? No.
(2) Can a physicist develop new instruments and methods for diagnosing disease? Yes.
(3) Can a physicist develop models to improve the diagnosis of disease? Yes.
(b) Engineering.
(1) Can a physicist specify the motors to be installed in a building to operate the elevators? No.
(2) Can a physicist design a new type of motor? Yes.
(3) Can a physicist specify the grade of concrete to be poured in the foundation of a new building? No.
(4) Can a physicist develop an improved grade of concrete? Yes.
With respect to the initial question about physicists working on Wall Street: Yes they do. Some analyze financial data. Some develop predictive models about how portfolios will behave, when to sell, when to buy. Some work as analysts for venture capital firms. Other physicists work for insurance and credit-card companies doing risk analysis and predictive modelling. Here's a story in APS News of a physicist who went from chaos theory to credit-card fraud prevention:
https://www.aps.org/publications/apsnews/201701/profiles.cfm
[By the way, APS News presents columns frequently on physicists working outside of what is considered mainstream physics. You should skim other previous issues as well (publically accessible).]
As for me personally (BS, MS, PhD all in physics), I've worked as a physicist, but also as a quality process engineer, systems architect and engineer, network architect and engineer, and patent agent. The architect and engineer jobs did not require any additional formalities. Working as a patent agent required me to pass the USPTO patent bar exam to get registration (a BS in physics met the requirements to take the exam; and I bought a self-study package to prep for the exam). But note, if you choose not to take the exam, you can work as a "technical specialist" in a law firm, and perform almost all the same functions and tasks as a patent agent ... except papers submitted to the patent office would need to be filed under the name of a registered practitioner (patent agent or patent attorney), who accepts final responsibility for the work.