If you look at most any vertical shaft engine, most all of them will 'weep' oil down the shaft over time and it attracts dirt and looks bad. To answer your question, I installed a seal on mine because I just didn't the dirt accumalation. Yes, if not careful, you can push the governor shaft into the engine because you have to remove the retainer clip that would otherwise prevent it from sliding into the case to install the seal. Honestly, I found it to be a challenge to get that lil' seal installed without damage of issue and found it easier to remove the engine and drop the pan from the start.
The casting for a seal is there because Honda offers an engine type that is designed to run at up to 45 degrees (cylinder up) and it is necessary to seal it as the oil level will be well above the governor shaft at that angle.