Only tires with sufficient inflation pressure can bear the weight of a bicycle. The following applies for the road: The higher the inflation pressure the lower the rolling resistance of the tire. The susceptibility to punctures is also lower with high pressure.
If the inflation pressure is continuously too low, premature tire wear is the result. Cracking of the sidewall is the typical consequence. Abrasion is also unnecessarily high.
On the other hand, an under-inflated tire absorbs road shocks better. Wide tires are generally used at low pressure. The larger air volume is advantageous in that it absorbs road bumps and holes, but does not suffer from higher rolling resistance, less puncture protection or low tire wear.