I agree that pack animals are a problem. In my opinion they should only be allowed in designated wilderness areas on trails specifically designed for pack animals and only by special permit--limited to people with documented physical disabilities and their guides.
Obviously wildfire events are special cases where mechanized equipment is allowed although obviously the least damage that is done the better. 
Bicycles are not "small potatoes" and it is a spurious to compare them to vehicles used in exceptional events like wildfires. Footpaths are designed for human feet not mechanized vehicles which belong on roads and specifically reserved, less pristine paths. Bicyclists are not welcome in the backcountry and will be kept out by whatever means necessary.