Can Cosmic Microwave Background Radiation be Measured, Really?

The Cosmic Microwave Background radiation CMB is supposed to be a 14 billion year after-glow with perfect Planck blackbody spectrum at temperature $T=2.725$ Kelvin K of a Universe at $T=3000$ K dating back to 380.000 years after Big Bang. The apparent 1000-fold temperature drop from 3000 to 3 K is supposed to be the results of an expansion and not cooling.  

To get an idea of the magnitude of CMB let us recall that a Planck spectrum at temperature $T$ stretches over frequencies $\nu\sim T$ and  reaches maximum radiation intensity $E\sim T^3$ near the end with a high frequency cut-off over an interval $\frac{\nu}{T}\sim 1$ (notice exponential scale):

 

The $10^3$-fold temperature drop thus corresponds to a $10^9$ decrease of maximum intensity and $10^3$ decrease in spectrum width. Intensity over width decreases with a factor $10^6$ as a measure of precision in peak frequency. 

We understand that to draw conclusions concerning a 3000 K spectrum from a measured 3 K spectrum requires a very precision on the level of microKelvin or 0.000001 K. Is this really possible? Is it possible to reach the precision 2.725 K from intensity maximum? 

Why is modern physics focussed on measuring quantities which cannot be measured, like ghosts?

CMB was first detected as noise maybe from birds visiting antennas, but the noise persisted even after antennas were cleaned and then the conclusion was drawn that CMB must be left-over from Big Bang 14 billion years ago and not from any birds of today.  Big Bang is physics, while birds is ornithology.