Without asyncio memory consumption stays low and stable for me:

$ ./python -m venv venv
$ ./venv/bin/pip install psutil
$ ./venv/bin/python
>>> ssl.OPENSSL_VERSION
'OpenSSL 1.1.1g FIPS  21 Apr 2020'
>>> import psutil, ssl, os
>>> p = psutil.Process(os.getpid())
>>> cafile = ssl.get_default_verify_paths().cafile
>>> p.memory_info()
pmem(rss=14811136, vms=237223936, shared=8138752, text=2125824, lib=0, data=6701056, dirty=0)
>>> for i in range(1000):
...     ssl.SSLContext(ssl.PROTOCOL_TLS).load_verify_locations(cafile)
... 
>>> p.memory_info()
pmem(rss=17489920, vms=238170112, shared=9863168, text=2125824, lib=0, data=7647232, dirty=0)
>>> for i in range(1000):
...     ssl.SSLContext(ssl.PROTOCOL_TLS).load_verify_locations(cafile)
... 
>>> p.memory_info()
pmem(rss=17489920, vms=238170112, shared=9863168, text=2125824, lib=0, data=7647232, dirty=0)