There are 35000 thermal calories in 35 food calories and about 4184 Joules per thermal calorie. So unless I've made a mistake those 35 food calories represent almost 146 megajoules of energy. Burning 146 megajoules while covering one mile at a pace of 12 miles per hour, means that the cyclist is burning energy at a rate of about 12 megawatts; Considering the fact that, at best, 400 of those watts make it to the pedals, the loss is absolutely staggering, completely dwarfing any of the energy that actually makes it into the mechanical system.
And what are typical mechanical losses? 1 watt, 10 watts, maybe 100 watts for a rubbing brake? Think about it this way: a bicycle that is even 0.001% (one thousandth of one percent) ergonomically inferior is as inefficient as a rubbing brake. Muscular losses are clearly the overwhelmingly dominant source of inefficiency. Mechanical losses aren't even worth considering.