Hi, Is there any clear down sides if I would lowering the seat high of my bike with suspension lowering links (see the picture below)? Plus any extra harm if I would do just that (= leaving the front suspension as it is)?
You'll effectively change the rake on your steering head and slow down the steering if you leave the front standard. Also lowering the frame (suspension) will leave you with a side stand that's the wrong length, bike may not be safe on the stand.
By using lower dog-bone line, your ground clearance decreases, rear wheel get closer to the fender, side stand will make the bike stand taller unless shorten it or get new shorten stand. That also applies to center stand. It will be harder to put bike on the original stand unless you shorten/buy new shorter stand. By leaving the front suspension where it is while lowering the front, you are increasing the rake angle of the bike which means the turn in will be slightly sluggish (think cruiser vs sport bike) as for harming the bike...it is all about compromise. I would say as long as you can handle the new sluggish turn in, not doing more crazy things to bottom out your shock and try to go over the tallest rock, I would say make the bike fits you.
If short in the leg then thinner seat is a better solution than a lowering link. Less ground clearance for cornering, side and main stand issues plus slower steering will be need to be a consideration. Lowering the front end will need to be done if the original geometry is to be maintained which would be beneficial considering the research investment previously made by the manufacturer. Making the bike personally suit you is very important, off roading even more so as I've had plenty of off road bikes, however this needs a balanced solution and note, everything has a price.
There are very limited options for certain types of bikes for shorter riders though; so I would imagine that if you want to do a specific type of riding you have to buy the bike you feel is most suitable and make it fit as best you can. As the far more experienced people than me above state, everything has a price, but sometimes we have to compromise I think.
