To Preheat Or Not

I have seen (yeast) bread recipes that rely on an un-preheated oven and seem to take advantage of the slow heating process (give the leavener some time to act before incapacitating it by overheating). While pound cake is unlikely to use yeast, there was likely a similar idea on the recipe writers mind. Maybe getting a somewhat denser texture by firming the outer layer before activating the leavener in the core is the goal here. Such recipes tend to be unreliable because they make many assumptions about the bakeware and oven used.

EDIT: Another reason for somebody to develop a recipe that does not use preheating would be simply saving active time, especially for people having slow-to-preheat ovens - mix, put in cold oven, start oven, set a timer and step away.

One obvious reason is to avoid wasting energy. A lot of people tend to like recipes which avoid preheating for this reason alone.

But, assuming that there's more than that here, my guess is that the recipe is trying to use the slower heating as a way to achieve a greater rise. Whether your pound cake recipe relies on leavening (such as baking powder/soda) or whether it's a traditional pound cake recipe that relies only on the air bubbles beaten into the batter while mixing, a gradual temperature rise can in some circumstances result in more expansion.

Basically, baking is a race against time in crust formation vs. internal expansion. You want to allow enough time for the internal gas bubbles to expand and make the cake (or bread or whatever) lighter, because once the structure starts to harden (with egg coagulation, and then starch gelatinization), you can't expand any more. On the other hand, as a cake or loaf rises, it becomes increasingly unstable. If you wait too long to form a crust and then stabilize the internal structure, your whole cake could collapse.

Frequently, the inside portion of a cake or loaf continues to expand even after the crust hardens, resulting in cracking on the top surface (common in pound cakes, perhaps even desirable according to some). In extreme cases with things like yeast breads, it can even result in a "blow-out" where the pressure from internal expansion literally blows a big hole in the crust.

With pound cakes, this balance can be a particular problem. As already mentioned, hardening the crust too early can result in excessive cracking. But hardening the crust later can also be a problem if the internal structure is unevenly heated (and thus unevenly stable). If the crust hardens while the cake is rising very high (e.g., from rapid expansion under high oven heat), but the internal structure is unstable underneath and collapses a bit, it can result in the "crust separation" where there's an air gap between the top crust and the rest of the cake. It's possible that heating more slowly can make that less likely by heating the whole batter more evenly and ensuring the internal parts of the cake are closer to setting along with the top crust.

Anyhow, to generalize a bit more, one of the reasons to slowly heat a baked good is to try to allow more time for a gradual expansion. On the other hand, internal air within batter/dough will eventually "leak out." It's actually a continuous process, since batter/dough is permeable to air. With cake batter, you can often actually see bubbles rising and popping on the surface of a cake early in the baking process. So you need some structure and crust to form to prevent all that air from escaping and collapsing your batter too. The trick, again, is to balance the time given for bubbles to form/expand vs. how fast the cake sets (i.e., structure hardens). That's actually one of the primary reasons for different baking temperatures in different leavened baked goods.

While allowing expansion during preheating can sometimes be helpful, it's also hard to manage. Ovens don't preheat at the same rate. If your oven preheats too slowly, it could actually cause your batter to rise too much before it stabilizes, thus resulting in collapse. As pointed out in another answer, some ovens with radiant heat elements (especially electric models) can actually introduce a "broiling" effect on the outer surface during preheating, which could counteract the positive effects if the "broiled" crust hardens early and prevents further expansion.

Since it's less predictable, most recipes tend to recommend preheating for things like cakes and pastry. And no matter what, you'll have to monitor doneness more frequently the first few times you do a recipe like this in a particular oven, since the time window for being "done" will likely vary much more significantly for recipes that don't preheat.

Without seeing the recipe and likely experimenting, it is hard to know for sure, but a few thoughts on pre-heating:

The shorter a cooking time, typically the more important it is to preheat. If you are doing a 5 minute cookie bake, you are unlikely to get your desired results if you fail to pre-heat. If you are doing a 6 hour roast, well, you are probably just wasting energy preheating.

The general idea is, if your recipe calls for a temperature for 30 minutes, then it needs to be up to that temp and stable before you start. A counter argument is how can it be when you open the oven to put the item in and radically lower the temperature when you do that.

Part of the tradition of most recipes saying to pre-heat was wood stoves especially, but older models in general which heated slowly and one person's might take longer to come to temperature than someone else's. So, baking for 30 minutes in my stove that comes to temperature in 10 minutes would result in half cooked in someone else's over that took 20 minutes to come to temp, and burnt for someone else who pre-heated, so the pre-heat command put everyone on an even field. Today, most ovens heat up fairly quickly so it is less of an issue other than for shorter cooking times and things that need precision such as delicate pastries. BUT, and this is a big but, with many modern ovens which heat to temp quickly, they do so with higher power. So, if you put things, especially short cooking time items, rather than taking longer to cook, they will burn, but may also be half raw. While you have you oven set at say 350F, it may actually be pouring 500F heat at your dinner rolls until the full oven temp stabilizes, and you end up burning the surface while not getting the middle cooked.

Now, one reason I can think that a recipe might specifically say not to pre-heat would be to take advantage of this. That initial higher power while the oven is heating and stabilizing could help form a crisper crust and then allow the bulk of the cooking to occur at an effectively slightly lower temp, similar starting an item at a high temp and then allowing the temperature to fall as is sometimes done for a bread with a crisp shell like crust but delicate interior. The effect would be a lessor example of this.