Why can't I put food on the pan while the stove is heating up?

There is a simple fact which many intermediate cooks don't seem to realize:

The rate at which you pump heat into your food has a huge influence on what the end result tastes like.

So, if you put food into a cold pan, and it gets heated slowly, you end up with a different result than if you throw it into a hot pan that transmits a lot of heat into the food at once.

Both techniques have their place in the kitchen, but the "heat quickly" one usually produces results which the majority of people like - vegetables stay firmer, doughy foods get a nice crust, sticky things release easily, etc. So it is used more often. And if you want good results, I'd suggest to stick with your recipe and use a heated or cold pan as it directs you.

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.

One reason is to get a sear on the item being cooked. You don't add the oil to a cold pan because its easier to judge the temperature if the pan is empty (you can spritz water on it to see if its hot). After the oil is added, its given a few seconds to heat up (rippling means its hot) and then the food items are added. Its much more consistent if the pan is already at temperature and you'll be able to get a nice sear.

A lot of food you can cook from cold. Most if not all vegetables. I even cook a steak from cold (most people would not).

Brown ground meat for like spaghetti I like to start cold as I can better break it up as the fat begins to melt.

Some stuff will stick at lower temperatures. For me a low fat turkey burger will stick if I start cold.

Some times you want to brown and not cook the center much. I like this for asparagus. For that the pan and oil needs to be hot.

A pancake you need to cook hot.

Browning meat for slow cooking should be hot.

By heating first you can better set the temperature. If it is too hot you can cool it down before adding the food. If you cook from cold and it gets to hot you burn it. Cook from cold you need to know the stove setting.