I have my desktop system running continually without shutdown and I want to get normal times (3:01, 4:15, 5:30) for cron.(daily|weekly|monthly) jobs but when anacron is installed these jobs run at around 7:30 and there is seems to be no interval between daily/weekly/monthly jobs.
Is it safe to just remove anacron?
What else could be affected by change from anacron to regular cron?
As long as you don't have any additional schedules in /etc/anacrontab apart from daily, weekly and monthly, it should work out of the box without affecting anything except the runtimes for the daily/weekly/monthly schedules.. The default crontab checks if anacron is installed, and runs the mentioned schedules if anacron is missing from /usr/sbin/.
To be absolutely sure, you could do a soft removal by just stopping the anacron service with service anacron stop and remove test -x /usr/sbin/anacron || from the lines in /etc/crontab. When you are satisfied, you can remove the package.
