Better browning starts with less water, not necessarily more fire. Moisture collects its toll. Before a wet steak or mushroom can develop a crust, the pan must supply enough energy to evaporate the surface water, which diverts heat from raising the food's surface temperature. A paper towel removes that burden before the burner gets involved.
A hotter pan is often an expensive workaround. Water resists the rush. At atmospheric pressure, a water-covered surface tends to remain near water's boiling point, about 100 degrees Celsius, while evaporation consumes energy through the latent heat of vaporization. Browning wants higher temperatures. The Maillard reaction, in which amino compounds react with reducing sugars, accelerates markedly as a drying surface climbs above roughly 140 degrees Celsius, although it can occur below that temperature. Drying changes the timetable. Removing surface moisture lets more incoming heat raise the surface temperature instead of turning liquid into vapor.
Restraint can produce the more assertive crust. Excess heat has costs. Although raising the burner can speed evaporation, it may also overheat exposed oil, scorch already-dry patches, and overcook thin foods before wetter areas brown. Pat the surface dry. Then use a suitably preheated pan, avoid crowding that traps moisture and cools the cooking surface, and allow contact long enough for browning to develop before moving the food. Heat still matters greatly. But once surplus water is gone, the pan can spend less energy making steam and more developing flavor: the towel leaves no signature except the crust.