First, I made the following modification to resolve "TypeError: 'type' object is not subscriptable" using Pyston 2.3.5.

$ diff llil1.py llil2.py 
53c53
< def collect( data_list :list ) ->dict[ str, int ]:
---
> def collect( data_list :list ) ->dict:
87c87
< def process( cat_count :dict[ str, int ] ) ->Generator[ str, None, N
+one ]:
---
> def process( cat_count :dict ) ->Generator:
110c110
< def sort_native( cat_count :dict[ str, int ] ) ->list[ str ]:
---
> def sort_native( cat_count :dict ) ->list:
[download]

Python 3.10.7:

# I have pyston_lite_autoload installed already. It can be disabled.
$ DISABLE_PYSTON=1 python3 llil2.py big1.txt big2.txt big3.txt > out1.
+txt
collect time         :    5.1 s
sort+format time     :    3.6 s
total processing time:    8.7 s
output time          :    3.6 s
total time           :   12.2 s
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Python with Pyston-lite loaded automatically:

# Install pyston_lite_autoload to ~/.local/lib/python3.10/site-package
+s/.
$ python3 -m pip install --user pyston_lite_autoload

$ python3 llil2.py big1.txt big2.txt big3.txt > out2.txt
collect time         :    4.3 s
sort+format time     :    3.5 s
total processing time:    7.9 s
output time          :    3.3 s
total time           :   11.2 s
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Pyston 2.3.5:

$ ./pyston_2.3.5/bin/pyston3 llil2.py big1.txt big2.txt big3.txt > out
+3.txt
collect time         :    3.7 s
sort+format time     :    3.4 s
total processing time:    7.1 s
output time          :    3.0 s
total time           :   10.1 s
[download]

Pyston makes it all the more fun.