This is going to be a very long post so if you are too lazy to read, the answer is NO, WOT is not bad, if you want to know why then grab some popcorn and disconnect the phone.
First I would like to make a distinction, because I don't know what are you talking about and it seems like everybody is talking about two different things like is the same.
1.- WOT - Wide open throttle, which simply is pressing the accelerator fully, and this doesn't have a direct relation to the speed of the engine; you can go at wide open throttle and at a constant speed, like in an uphill section of a highway.
2.- Redline - Or maximum rpm which is taking the rotational speed of the engine to the limit imposed by the manufacturer (for example 6000 rpm); and this also doesn't have a direct relation with the position of the accelerator or the butterfly valve; you can go at 6000 rpm and not even touch the accelerator pedal like when you brake with the engine.
These two conditions can be confused as one single event by many people especially if they have a useless automatic transmission, but I will leave the automatic transmission rant for another time.
Anyway the question is, are any of these two conditions bad for your engine???
Let's start with what is bad for your engine?? The answer is lack of lubrication. And how an engine is lubricated?? An engine uses fluid bearings for that and there are two types, hydrostatic and hydrodynamic.
Hydrostatic bearings rely on an external pump to move the fluid into the bearing, (like the main bearings, the connecting rod bearings and the camshaft bearings), think of this bearings as a hovercraft, here a large fan pumps air to keep the ground and the bottom of the hovercraft separated and thus reducing the friction between them.
Hydrodynamic bearings use the motion of the surfaces to force the fluid into the bearing (like piston rings, wrist pins, camshaft lobes and valve stems), think of them as a hydroplaning car in which the forward velocity of the car has wedged a film of water between the tires and the road reducing the friction and preventing contact between the two.
Now, how can these modes of lubrication fail?? And leave the engine unprotected
1 Too much load, like if you put too much cargo in your hovercraft and it can't take off. In the engine is the equivalent of too much pressure in the piston.
2. Not enough fluid, like the fan in the hovercraft is not spinning fast enough or there isn't too much rain to make the car aquaplane. In the engine is the equivalent of an undersized oil pump or the oil pump is not going fast enough.
3. Not enough velocity. Like if the car is traveling through a massive rain storm but is not going fast enough to hydroplane. In the engine the equivalent is a very slow rotational speed like less than 500 rpm.
Now to simplify the things more modes 2 and 3 are linked via the oil pump because the pump is connected to the crankshaft so the faster the engine is going the more oil is pumping through the engine. Think of this in our example of the aquaplaning car as the faster the car is going the more it rains in the road so this always ensures that the car is aquaplaning.
So now we only have two modes of failure: 1) too much load and 2) not enough oil.
Fortunately for you, your friendly neighborhood team of engineers took into account all this any many more variables to design your engine and they came up with specifications for the oil pump, bearings, piston rings and the oil that Is going to be used with that engine.
Now to answer our original question how can WOT or redlining our engine can produce these failures in lubrication???
Let's start with WOT. Since those dashing engineers took into account the maximum force applied into the piston and design the lubrication system with enough capacity to withstand this load we can safely say that you can go at wide open throttle through the whole rpm range and you are not going to have any problem with the engine. It's like our hovercraft has a maximum weight capacity of 3000 tons and you put 3000 tons of stuff in it, then of course that is going to fly without any problem.
Now redlining your engine, well, as I said before the faster the engine is going, the more lubrication it gets. So you can hit the redline as many times as you want and nothing will happen to the engine. But then you ask why I can't go beyond that maximum rotational speed?? We'll that is because the inertial forces (that arise because the piston needs to stop and then accelerate in the other direction and the stop again and so on) will increase in magnitude and frequency and that would lead to material fatigue and eventually a blown engine.
Now I can hear you all scream: yeah we already knew all that!! but the OP asked about a cold engine and short trips what about that????
The problem with the oil is that it increases it's viscosity when it cools down, so, how this affects the lubrication of the engine? well when the viscosity increases it takes more energy to pump the same amount of oil and that means that the pump needs to apply more pressure, to protect the pump from excessive pressure those brilliant engineers put a valve that opens when the pressure is high and part of the oil goes to the engine and another part goes back into the oil pan, so in that case the amount of oil circulating through the engine is less than the amount that our magnificent engineers deemed proper for that engine; so in our examples the hovercraft is dragging its bottom across the ground and the car is not hydroplaning and the wheels are making contact with the road, so in this case, yes, you have wear, and your engine will suffer for this condition. Once that the oil is hot and it's viscosity has decreased then this is no longer a problem. *(Some engines use this valve even when the oil is hot, but that will be covered in another post)
Now you probably are going to ask: at what temperature my oil is hot enough to avoid this terrible condition???
We'll you can know that only if you install an oil pressure gauge and an oil temperature gauge and noting at various oil temperatures from what engine speed the oil pressure remains constant, for example an engine that when hot produces 10 psi for every 1000 rpm so the oil pressure goes from 10 at idle to 60 psi at the rev limiter; but when is cold at idle the pressure is 20 psi and from 3000 rpm the pressure remains constant at 60 psi. Then I would recommend to you to not let the engine go beyond 3000 rpm until it gets warmer. There will be a temperature when the relief valve does not activate and from this temperature onwards the engine is properly lubricated and can go at WOT or redline.
Depending on the type of oil you use you will get different values for this temperature, for example, a single grade oil does not activate the relief valve from 85 °C, a multigrade oil from 70 °C and a synthetic oil from 65 °C so if you use synthetic oil you will cause less wear in the engine.
So I think this is enough for now, and if you read through all of this and you are still concious, CONGRATULATIONS!!!! You are a maniac about motor oil. Say it loud and say it proud.