A front wheel caliper brake merely scrapes mud off the wheel and clogs up.
Some pushchairs are designed for jogging but are sold in the UK as All Terrain Pushchairs. They have a front wheel caliper brake but if you take it off road after rain it will quickly clog up with mud.
You can normally remove them as there will also be a rear wheel brake so that it complies with BS7409.
Unless you are running at serious speed you don't need a brake to slow down and many of our customers jog with their Land Rover ATP (Manufactured by Pegasus Pushchairs Ltd under licence by Land Rover until September 2002, but no longer available and having no association with the current owner of the Land Rover Trademark).