Slower charge is less stress and heat so that translate to better life. They should make charging dual mode where it'll take into account location and time to choose between quick such as in office/car and normal at home before bed and with manual override. Alaternatively, if the battery is replaceable you can always quick charge and replace more often.
I think it would be highly dependent on the battery technology itself and if it was designed for quick charging and whilst there may be some element of truth in what your relatives are saying in regards to overall battery health in the long term - it may only be applicable in certain scenarios - whilst in others - quick charging would have little to no difference to the overall speed at which a phone then 'discharges'. A 70% battery will discharge at the same rate whether it got to 70% by quick charge or slow charge. So unless the overall battery health was somehow impaired over time charging your phone by quick charge or slow charge will not affect the rate at which the device then discharges.
I think it would be highly dependent on the battery technology itself and if it was designed for quick charging and whilst there may be some element of truth in what your relatives are saying in regards to overall battery health in the long term - it may only be applicable in certain scenarios - whilst in others - quick charging would have little to no difference to the overall speed at which a phone then 'discharges'. A 70% battery will discharge at the same rate whether it got to 70% by quick charge or slow charge. So unless the overall battery health was somehow impaired over time charging your phone by quick charge or slow charge will not affect the rate at which the device then discharges.
There is research underway that may change the way li-ion batteries are charged. This research suggests li-ion cels can be charged at a much faster rate than currently charged without damaging the cells. We'll see what the future holds.