Volume. 1GB of data per day is rounding error. If you have tens of thousands of servers, each generating hundreds of gigabytes of data per day, tail -f and grep don't scale especially well.
Recall that the poster said this was for a small startup. If you're Google, by all means, use Google logging tools. If you aren't, then solve the problem you have, not the problem your résumé needs.
> Twenty years later, I still can't fathom why we're spending so much money on Splunk, DataDog a the like.
And the poster above answered that question
mkdir -p /tmp/ssh_output
while read ssh_host; do
ssh "$ssh_host" grep 'keyword' /var/my/app.log > "/tmp/ssh_output/${ssh_host}.log" &
done < ssh_hosts.txt
wait
cat /tmp/ssh_output/*.log
rm -rf /tmp/ssh_output