Maybe you should tell that to all those multi-LED flashlight manufacturers, whose products you see everywhere these days. I don't think they have many problems with LEDs in parallel.
This is starting to look like another of those oft-repeated urban legends that people believe is true just because they're heard it so many times.
Show me a peer-reviewed paper that explains why this is a bad practice and I might believe you. Otherwise, I think this advice can be safely ignored.
You are not going to find peer-reviewed published papers. This is engineering not science.
A lot of equipment is not well engineered. I have seen commercial products with LEDs that have failed within a few days because they paralleled LEDs and did not work out how the current would be shared. On other products the brightness LEDs was different because the current shared unequally.
It all depends on the slope of the I/V graph of the LEDs, in effect the resistance of the LEDs. Some power LEDs can be run at quite high current, and they have significant resistance, so that they are safe to run at voltages quite a lot higher than the voltage that they first conduct at.
For example,
https://www.farnell.com/datasheets/457476.pdf is designed to run at 150 mA, and the typical graph (figure 3) shows about 3.4 V, and maybe 100 mA at 3.2 V
The forward voltage will change with temperature. Figure 9 shows that the voltage will fall by about 0.05 V if the temperature rises by 40 deg C. If you put two in parallel, the hotter one will have a lower voltage and it will take more current than the colder one. That can lead to temperature imbalance and thermal runaway, but it very much depends on what heatsink there is.
There is then the problem of any voltage drop in the wires between the LEDs. Obviously a small voltage drop can lead to a large difference in current.
Finally, there is the problem of forward voltage variation within batches of LEDs. Those ones show the typical voltage is 3.4 V but the maximum is 3.8 V at 150 mA. A quick look at figure 3 shows that if you feed one of those LEDs that has forward voltage of 3.4 V with 3.8 V, it will take 300mA. I'll guess that it will last for a second or two at that voltage.
If you look at lower power LEDs, the problem is much worse.
https://www.farnell.com/datasheets/80864.pdf That is one of the few low power LEDs where the manufacturer has bothered to include a V/I graph.
It is very steep, in that the current shown in figure 2 goes from 10 to 20 mA over about 0.1 V. There is also a huge possible variation of forward voltages, as they quote 1.6 V to 2.4 V as the acceptable range. I realise that the actual variation will be a lot less, but without knowing what it is in practice, you can't go and assume that the variation will be less than 10% of what the manufacturer says it might be.
Now I accept that a torch, if well engineered, can parallel the LEDs. The heatsink characteristics will be known. The voltage drops will be considered, and the LEDs may be sorted before manufacture to make sure that the forward voltages are close together within any one torch.
I also realise that you could easily take a few LEDs, especially if they came from the same batch, and if you don't run them near their limit, and put them in parallel and it would work. That does not mean that you could do it every time, and it certainly does not mean that if you replaced one of the LEDs with one from another batch that it would continue to work. If you are making one-off projects, it is your risk and it's only a few LEDs, and that's fine. You are just trusting that the LED currents will be near enough the same. That is not engineering, it is luck if it happens to work.
This forum has a lot of readers who are learning the basic rules. If you stick to putting LEDs in series, the current in each LED will be the same whatever. That is a very simple rule, and a far greater proportion of readers can follow that one rule than can, or want to, consider variations of temperature, variations within batches and voltage drops that are needed to safely run LEDs in parallel.
The circuit diagram for LEDs in parallel does not show any of the considerations that are vital for getting the circuit to work reliably in practice. That is another reason why, even in the commercial environment, a designer would put LEDs in series. The designer can be sure that if the circuit is followed, the current in each LED will be the same. If the design has them in parallel, the circuit diagram has to be accompanied by pages of other rules about temperature equalisation, interconnection resistance and LED choice.
I've made lots of circuits with LEDs, but I have never been in a situation where the cost of working out whether they are safe to go in parallel is less than the cost of putting them in series. If I were a designer for a product that were to be made in thousands, I would do all the calculations and tests, and I might go for parallel LEDs. Even then, the increase in time taken to get the product to market might make that approach stupid.