One important aspect is the geographical restrictions. Not all countries are having ICAO accredited english language testing centers. Anyway IELTS scores of above 6 are being considered as equal to ICAO Level 6 in some countries.

 Apart from geographical limitations, English used in the testing is normally different from the one we are going to use in everyday R/T and particularly in emergency situations. Instead of evaluating every day English usage, an internationally accepted R/T license or exam will be a better option.

It's importance as a common communication method cannot be understated.  It's adoption is due to NATO being dominated by the US & the UK and ICAO following suit later.

However a case could be made that the language used for flight communications is not english but a highly formalized subset of english.  I would agree that an assessment of the english that will actually be used in cockpit operations is more appropriate but communication is not always limited to these formalized subsets and broad knowledge of english can only be an advantage when the situation does not conform to "normal".  In an emergency a good grasp of english would be essential to communicate the situation to the ground clearly and effectively as the odds are good that the only common language you share with ATC is english.

The main problem is that English is a very rich language with many words with the same meaning. Also the language can be very subtle. Many documents written in English tend to be very complicated in structure which make them difficult to read by people where English is not their first language.

My last 8 years of working life were spent as a university lecturer. I developed a course in technical authorship. In it I introduced students to "Plain English" and "Simplified English". The latter was developed in The Netherlands specifically for the aeronautical industry and aimed at maintenance documentation.

I have over 45 years experience of aeronautical engineering, both flying and engineering, and fully appreciate the importance of clearly written procedures. On a visit to Crossair in Switzerland some years ago one of the managers (with English as his third language) I dealt with asked if our technical authors took delight in using different words with the same meaning. e.g. repair, mend, fix. Simplified English should have been used as it demand consistency in the meaning of words.

I took the message back to the company that I worked for. Our technical authors had not been trained to develop documents in Simplified English. That deficiency was corrected.

I agree with the previous answer, the aviation world needs a specialist sub set of the English language. In the days of wireless operators using Morse code the "Q" codes offered a specialist subset. of course some of those codes are still used verbally e.g. QNH.