In the UK we have shared cycle paths. These are wider pavements that pedestrians also use. This is good, but not always. I had a pedestrian tell me off for riding on the path, standing right under the shared path sign. Duh. Also, cycle lanes tend to be at the side of the road, where all of the junk from the road ends up, as well as having to navigate Iron works. Other lanes that I have ridden on have such obstacles as freshly cut thorns from hedges, low laying branches, roots, pot holes, ice etc. No the gritters do not do the cycle lanes. So when I ride on the road, it is for a reason. Another problem with urban cycle paths is that you have to stop and look both ways every time you come to a junction. If I were on the road, I would not have that issue and other traffic would have to deal with me as a vehicle.
OK legal definition time. The car, in the UK is officially designated as a carriage. This came in during the early 20th century as some bloke named Benze had a breakthrough in his garden shed. Here is the thing. Cycles are also legally designated as carriages and have been so since the mid 19th century. So we were here first.
Now for the slowing you down bit. I have driven commercially, running my own diary and visiting companies. I would always allow extra time to get to the client, to allow for road works etc. Its called planning. Perhaps you should try it. If you left earlier you would not get so stressed.
But here is the real rub. I cycle, keep fit and help to keep my heart in good condition. You get stressed and angry. Bad news. I am going to outlive you. So rant all you want, but the last laugh will not be yours.