Requests / Asyncio: Is there a drawback for making pool_maxsize=1000 with a Python requests session?

I am using the following code to increase the pool maxsize with requests:

import requests
session = requests.Session()
session.mount("https://", requests.adapters.HTTPAdapter(pool_maxsize=50))
session.mount("http://", requests.adapters.HTTPAdapter(pool_maxsize=50))

Is there a drawback to settings pool_maxsize=1000?

I sometimes need 50 - 1000 connections, but most of the time I only need 1 connection.

Alternatively, is there a way to allow dynamic pool sizing?

Which solution is best:

1. Set pool_maxsize = 1000
2. Create 2 sessions, 1 with pool_maxsize = 1 and the other with pool_maxsize=1000.
3. Dynamically alter pool_maxsize as and when I need a different number of connections. (if possible)

Speed is paramount!

Edit: Most of the time I'm doing normal requests:

session.get(....)

But sometimes I am using asyncio where I will have a large number of requests to carry out:

import asyncio
async def perform_async_calls(self, session, urls):
    loop = asyncio.get_event_loop()
    futures = []
    for url in urls:
        futures.append(loop.run_in_executor(None, session.get, url)

    results = []
    for future in futures:
        result = await future
        results.append(result.json())

    return results

from Requests / Asyncio: Is there a drawback for making pool_maxsize=1000 with a Python requests session?