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Black Hole Mass Calculation

Do cosmologists actually calculate the mass for a proposed super massive black hole at the center of a very distant galaxy or is it just a guess?

from I found:

You can calculate the mass of a supermassive black hole from the orbit of a star orbiting the black hole.

You can calculate the mass of an object from the orbit of a body orbiting around it. A form of Kepler's third law is
a^3 = M T ^ 2
. Where
a  is the semi-major axis distance in AU, M is the mass of the central body in Solar masses and
T is the orbital period in years.

Evidence for the supermassive black hole at the centre of our galaxy, Sagittarius A*, came from the discovery of several fast moving stars orbiting the centre of the galaxy. One of the first ones to be discovered is called S2. It has a period of about 15.56 years and a semi-major axis of about 1,000AU.

In other words, to calculate the mass of a black hole at the center of a galaxy astronomers must 1) find a star rotating in orbit around it, 2) measure both its orbital period, and its semi-major axis.
Finding just a nearby star is not enough; it must be in an orbit that must be measured.

The accuracy of the Black Hole mass calculation is directly related to the measurements of an individual nearby orbiting star.

Putting the figures into Kepler's equation
1000 ^ 3 = 15.56^2 M
This gives the value of
M =4,130,000 solar masses.
Current estimates for the mass of Sagittarius A* are 4,300,000 solar masses.

These orbit measurements are probably possible with S2 given the wide range of visual technologies available to apply considering its Milky Way location and its distance, like infrared, UV, X-ray, etc. This must have been difficult given the center of our galaxy is so cluttered with stars and dust.

I can only assume this effort is magnitudes more difficult when the galaxy is very far away.

My big question:

Have we really found an individual star rotating around each distant galaxy center and made those required measurements for that star to make a valid calculation of mass?

I have some doubt after looking at pictures of distant galaxies with dense galactic cores. Is our current array of technologies really providing that extreme resolution with sufficient images over time (in years) to make these required orbit measurements?

Maybe I am totally wrong with my skepticism but when a SMBH is proposed for nearly every galaxy in the universe even when very distant I should be.

Shortly (02/10/2019) after the above post I discovered the S2 orbit was invalid and should not be used in the above equation.

On that date I also added the following comment to the above post.

For the claimed S2 orbit parameters to conform to Kepler's 3rd law:

S2 Period of 15.56 years would be a diameter of 6.3 AU.
S2 diameter of 1000 AU would require about 30300 years..

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