I read in the caveats the following:
PHP’s internal zlib compression must be disabled for the WP-Cache compression to work. Look in your php.ini for the zlib.output_compression and zlib.output_compression_level directives and comment them out by placing a “;” at the start of each line.
My host, named OVH, is one of the biggest in Europe (2 to 3 times bigger than famous US companies, just to say it is not a cheap small one), and it is impossible to change the php.ini file or declare it in a htaccess file for websites hosted on mutualized servers. So it is impossible to deactivate zlib compression. WP-Cache is working great with this host.
Before installing supercache and breaking everything, my question is: is there an easy way to circumvent this problem ?