Question

Why does a country having a large latitudinal extent have only one standard time​

Answer 1

Because if the country not have standard time. ... Because in a whole country there are different times in different time. The standard time is taken from the middle latitude of that country.

Answer 2

ᴀɴsᴡᴇʀ⤵️

That's why countries with large latitudinal extension,have a variety local times in it's own land territory. In order to avoid the confusion of the time difference in a same country,these countries use an average standard time.