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From mouse to moose,yes. My first moose rifle was a Sako 30-06,got a few moose and got birds too. I have then switched to 300 WM for better long range accuracy,easier trajectory and more power.
But a 30-06 can do it all at normal hunting ranges. I have done quite a bit "cleanup" work,we never leave a possibly wounded animal out there. When it is confirmed wounded,we follow the situation 24/7. My furthest moose has been 340 meters,300WM, I practise 300-500 regularly. My skills with a 30-06 wouldn't cut it.