Rasterio modifying JP2000 values

I am trying to mask out some of the Sentinel-2 L1C Bands prior to other applications that require me to keep the classic .SAFE structure of the data.

I usually use rasterio with no trouble, but even with an operation as simple as

import rasterio as rio 

input_band = ".../T33NVE_20180101T091351_B02.jp2"
out = ".../test"

with rio.open(input_band) as src:
    data = src.read()
    prof = src.profile
    
with rio.open(out, mode='w', **prof) as dst:
    dst.write(data)    

Here is what I get :

Input Image :

Output Image

I know JP2000 is a lossy format, and I don’t usually use it….
What can I do to end up with the jp2 files recognized by Sen2cor?

profile.update({
    'QUALITY': '100',
    'REVERSIBLE': 'YES',
})