Loud speakers are used for convenience. Take a note,
Without them the Imam had to put in a lot of effort to make his voice reach the last qatar of the mosque.
For large congregational prayers Mukabbir
(a person from the muktadi assigned to repeat the takbeers)can be assigned from the muktadi. But the problem is, not all the people who are attending the prayers are well educated on the masail of this act. So there is a potential chance of huge mishap if the mukabbir fails to do his duty accordingly.
There may be some other reasons also. For this convenience and inconvenience stated above, all the localities who are able to afford a loud speaker use them in mosques all over the world to ease the flow of takbeers.
But using loud speakers are not mandatory. People use them for convenience.
Everyone should act responsibly and show tolerance and respect.
The members of the locality should eagerly join congregational prayers. If anyone attends the prayers with takbeer-e-ula then how will he feel disturbed?
(because he is already in the mosque!)
In average it takes no more than 34 minutes on average in a whole day to complete the congregational prayers. Among them only 6 raka'ats throughout the whole day have loud reciting. If we accept that inconvenience then it would be a very remarkable example of communal harmony.
Also those who are using the loud speakers should be sensible. I've heard this in multiple occasions from multiple scholars that, "The use of loud speakers should be limited for adhan and congregational prayers." Different prominent scholars strongly condemn the misuse of loud speakers. For any gathering or bayan, the sound must be confined within the gathering. To use loud speakers throughout the streets is not welcomed at all.
In case we have any such issue in our locality, we should ask any elder or acceptable Ulama to look into the matter.