Black ink limit in press?

Cheap paper (newsprint especially) can literally fly apart on a press if there is too much ink, causing it to disintegrate at the speed it runs. It could be maybe moving at 30 mph or more, and this is no joke for anyone nearby.  But there is no problem with solid black, if you get the ink mix correct (they would want you to use 100%K for cost reasons).

"Does it cost more or is it hardly possible or it's not true at all?"

If the printer you are dealing with estimates the job based on what you plan do do with it, i.e. you tell them you are going to have many pages of full-colour solid backgrounds, etc, they WILL estimate accordingly, as they add in the cost of a certain weight of ink for the entire job (normally based on an average coverage for the type of content. i.e a full colour job will obviously involve more ink than a black-only text-based document).

Also, for images the ink limit is handled by the destination CMYK profile on a color conversion, so if you are converting to CMYK either in Photoshop or on a PDF export, it would be important to know what CMYK profile to use for the conversions so that you don’t exceed your printer’s TAC and create a drying problem—for example the default US Web Coated SWOP has a limit of 300%, while US Sheetfed Coated allows 350%.

Once you are in CMYK mode in either InDesign or Photoshop the assigned CMYK profile doesn’t prevent you from color correcting to, or building CMYK values that exceed the profile’s limit. The assigned CMYK profile also displays the expected difference between black only and black with CMY. Here is Coated GRACoL 2006 with InDesign’s Appearance of Black Preference set to Display All Blacks Accurately :

It has nothing to do with cost but rather the reality that paper can only soak up so much ink. The generally accepted standard is about 300% or so, depending on the paper. Glossier stocks have less ability. So, yes, it is preferable to have a "rich" black for large background areas, you just have to make sure the combination of CMYK inks does not exceed that limit. for instance 40C 30M 30Y 100K gives a nice rich black in print, but totals only 200% ink. A dark black in a photo may convert to something like 75C 65M 65Y 85K after it goes through color management.