I think it's important that those of us that aren't native English (myself included) have to also remember that when on-duty we have to react to things pretty quickly which includes trying to de-escalate and prevent dangerous scenarios from happening. You have to be crystal clear in your text to ensure no wires are crossed and that every party understands what you're saying. On top of that, you need to relay your messages quickly as time is of the essence and not everyone will have the patience for you to sit and think of a reply.
It can be stressful for a non-native English person to jump into the role of an officer where you deal with a lot more situations than you would if you were playing a random civilian. On top of the in-game situations, we have a tonne of OOC work with Incident Reports, Arrest Reports, Traffic Reports, Impound Reports, Death Reports - it's a heck of a lot of writing that other people /need/ to be able to read without struggling to understand what has been written down. So while I can understand your frustration (I've been there myself), I think it's important that a certain standard is upheld.
We actually have a lot of people from Europe that aren't native English speakers. Teamspeak is a wide variety of Europeans and finding an American is actually pretty rare! (I know this because we desperately tried to find American's to record voice lines in the LSPD video and it was a nightmare!)
Being on a roleplay server gives you the perfect opportunity to better your English. When I started roleplaying back during SA:MP days, my English was awful! I only ever played mute characters at the start and focused on my /me's. Eventually I would introduce characters that knew very little English until I felt comfortable with progressing.
I admire /anyone/ attempting to better their English on the server and I will personally stand there all day to not pressure someone into feeling like they have to rush or are being judged. But a certain standard must be met if you're going to be representing a faction such as the LSPD and as much as it's difficult to hear, I think it's a reasonable requirement on behalf of the recruitment team.
Roleplay is amazing because it let's you practice your English while having fun!