WhatALoad - grieving is different for everyone, and for many people, cars overtaking and cutting into the cortege is upsetting and disrespectful. Since there is no way of knowing whether the deceased or their relatives are, like you, unworried by this behaviour, or whether the mourners will be upset if you overtake, surely the best option is to err on the side of caution and hang back.
When my father died, we didn't have a cortege to take us to the church. Owing to scheduling issues, and the distance from the country church to the crematorium, we decided to have the post-funeral meal after the church service and before the cremation (the latter was only for close family, so everyone got to have something to eat and drink, and a chance to talk, before some of us headed for the crematorium, and the rest went home.
All this is background to what happened immediately after the church service. Dad was being taken back to the funeral director's chapel of rest, and would then be brought to the crematorium at the right time, so the hearse moved off from the church, and with no planning at all, everyone else fell in behind it, and we ended up with a cortege that traveled to the junction a mile from the church, where the hearse went right and we all went left.
I had no idea that this was going to happen, and when we turned left, I looked back and saw the cortege coming down the road we had just left, and that procession of cars really touched my heart in a way I cannot explain - I guess it was a last gesture of respect and affection from everyone towards my dad - in fact, 15 years on, just typing this has brought a lump to my throat and a tear to my eye again.
If that procession had been disrupted by some arsehole driving aggressively and putting their desire to get wherever ahead of what my dad's friends were doing for him and for his family, I would have been irrationally upset by that.
Funerals are generally a difficult, emotionally fraught time - surely everyone can understand and accept that - and whilst overtaking the hearse and cortege might not upset the mourners, hanging back and showing a bit of respect is much less likely to upset them, on a day which is upsetting enough as it is. And I would rather be a bit too thoughtful and respectful than not enough.