Because lined horses are already trained throughout a generation (or many) in a certain discipline, which may be the completely wrong stats for what a buyer wants. For example when purchasing brumbies from Wild Brumby, I have to start from scratch because Brumby trains them in barrel racing and I train them in dressage, so when it comes to breeding the horse I've purchased to my own herd, that generation will be worse than the previous one instead of better. I do it anyway for the graded in colours I'm missing, but if there weren't colours I wanted that can't be obtained in the wild, then buying a lined brumby would be entirely pointless and set my herd back a generation or two. A wild horse that I can train up to match my herd's stats is far better, as I can make sure it only gets PS in the correct stats. 

The other factor is colour! If a horse has been bred a few generations, then it's less likely to be carrying any hidden variations due to their low chance of being passed on. Hidden Dapples too is less likely. I've had wilds that have had 4-5 different hidden variations that I've only discovered by breeding them to my herd, and some breeds I'll buy wilds just to test if they're dapple carriers. 

So in conclusion people prefer wilds as they're a blank slate to train + they more often than not carry hidden genes that are usually not found in lined horses 

To add to what Mouse said, there is also the aspect of some people are looking for new bloodlines or to start herds from scratch.     This isnt the case for all players, and some of this may be seen more in breeds like say Arabians or TBs where a lot of lined horses at some point are very quickly related unless you are very careful with breeding.    Again, not all players care about this though.  

I for example wont breed horses (except the occasional whoopsie I will beat myself up over) if they share any relatives in x number of gens back.   (Normally the initial family tree page unless I see something REALLY fishy)    In some breeds its pretty easy to find new lined horses to breed to or pick up that fit what I need to help keep getting better and better stats.   But in other breeds, this is a lot more difficult, so I am constantly making sure I have lines that are new but still good to incorporate.   

It really all comes down to the player, how they play, what they are looking for, etc.  But Wilds and even Foundations can offer a lot of different things to different people :)

Thanks for the explanation. I mostly just breed for colour whilst trying to make sure my horses are above 4*, have roughly 300 to 500 PS when born, and are around 40 to 50 levels.

I remember hearing about people not breeding lined to prevent inbreeding but personally I have never bothered much since the game doesn't actually have any downsides (that I'm aware of right now anyways) to let's say breeding an aunt and nephew.

Also on the hidden dapples and things like that I have ended up finding hidden dapples in a horse I have had for like 8 generations (happened recently with my brumby collection) or I just go by off colour bred horses. I get why you'd want to check.

Anyways thank for response

-FaminesRose responding from Alt

No problem!     You are correct in that the game has no downsides to inbreeding.   That aspect is where you get a divide in play styles.    There is a part of the community that doesn't care, inbreeding isn't a concern, and so they dont watch for those things.    Then there is the other part of the community that does care, inbreeding to varying extents is a turn away, and they do watch for things like that when buying lined horses.      As long you play how you enjoy though thats the important part :D   But it can skew things with the horse market since so many people play in different ways, with different wants, needs, and goals.    It can be helpful to pick up on things like that though especially when selling horses because some horses may sell faster than others based on like 20 million different factors