In short, no, it has nothing to do with wanting to make recent logs easier to access.
Rather, daemons will often continue writing to the logfiles after they've been renamed, and sometimes for a long time.
Once a log file gets compressed (which really means writing a new file and deleting the old one) anything subsequently written to the original - now-deleted - file would be lost when the logfile is finally closed.
Sometimes a daemon can get "stuck" and refuse to close its log file. If that happens you might see this:
$ pid=$(pidof your_daemon)
$ ls -l /proc/$pid/fd/* | grep log
l-wx------ 1 root root 123456789 Jan 10 17:54 /proc/1234/fd/6 -> /var/log/your_daemon.log (deleted)
$ ls -lL /proc/$pid/fd/6 /var/log/your_daemon.log
-rw-r----- 0 root root 123456789 Jan 10 17:54 /proc/1234/fd/6
-rw-r----- 1 root root 0 Jan 10 01:04 /var/log/your_daemon.log
$ cmp /proc/$pid/fd/6 <( gunzip < /var/log/your_daemon.log.2.gz )
cmp: EOF on /dev/fd/63
/proc/$pid/fd/6
is still open and being written to but its link count is 0 - it has no names in the filesystem;
/var/log/your_daemon.log
is empty (size 0) because nothing is writing to it;
/var/log/your_daemon.2.gz
is a compressed copy of the log at the time the compression was done; its content is identical to the open log file, up to the point where it's truncated.
Anything past the truncation will be permanently lost once the open-but-unlinked logfile is closed.