There are many reasons for this and some apply only in some cases, but a few off the top of the head:
Very few applications would find it appropriate to put anything into cold oils if the item is in any way porous as it will absorb some oil and result in a greasy product while hot oil helps to seal the cooking item and reduce this tendency.
Oils that solidify are not likely to coat the pan and a good coating and hot searing are main sources for the non-stick quality, one of the points of oil in the pan for many applications.
Most cooks, even when using temperature as a guide have a general sense of how long to cook and item, and this almost always is from starting form a hot medium, not a cold one and adding the warm up time for the pan and other items as an unknown.
Often, slow cooking during a warm-up phase has very different cooking results than cooking in a medium which is already at temperature. This includes the lower temp environment has less ability to penetrate the item, so only the outside will initially start to cook, leaving that area done and likely over done too long before the interior.
With many items, especially those cooked in oil, low temperature will result in soggy items while oil cooking is usually meant for crisp results. An item that was allowed to become soggy and oil soaked by early low temps will seldom be salvaged by the temps rising later in the cooking.
Oils like olive oil and butter have low smoke and/or scorch points, so adding them before the pan is hot will often result in burned butter, smoked oil, etc. and bitter to ruined results, so the pan is brought to temp, the fat is added and given a briefer time to heat, then the ingredients go into the heat to sear, saute, fry or whatever the technique in use.
Techniques such as confi are a different process and one exception, and many other reasons may also apply, but that is a quick set off the cuff.