I read the logs from my servers. The amount of time I spend reading log summaries is determined by how important the server is. On the machines that are most important to me I carefully read log summaries and periodically scan the logs for anything that looks unusual.
The amount of time taken is obviously determined by the amount of data in the logs, so it is a benefit to me (in terms of spending less time) to have smaller logs. It’s also a benefit for me (and the other people who depend on those servers) that I spend my time on things that might be important instead of mindless failed attacks.
One thing that I do to reduce the size of my logs is to run sshd on a non-standard port. This requires using a Port directive in the file /etc/ssh/sshd_config and on the client machines I edit /etc/ssh/ssh_config to include a section such as the following to avoid the need to use the “-p” option for ssh (or the “-P” option for scp):
Incidentally I disable X11 forwarding explicitly because it’s a dangerous option which usually isn’t needed, and I specify the ssh-rsa algorithm not because it’s any better than the other option of ssh-dsa but because the possibility of having a secondary option that is normally used adds the possibility that a MITM  attack can be performed by an attacker who forces the client to use the non-default protocol (thus giving an unknown host key message instead of a message about an invalid key).
Note that these settings can go in /etc/ssh/ssh_config to apply to all users or in ~/.ssh/config to apply to only one user (IE if you aren’t root on the machine in question).
The practice of avoiding attacks by using non-standard ports is not Security by Obscurity in that the security of my systems does not rely on attackers not knowing the port. Attackers can easily scan all ports and discover which one I use. The fact is that any attacker who does so is a more serious threat than all the attackers who scan port 22 and bother someone else when they discover that nothing is listening, such an attacker deserves to have some of my time used to read the log files related to their attempt.