Because Lincoln perhaps more than any other President had an amazing insight into complex human problems, institutions, and laws, and the gift of writing to make them clear. It's what made him an excellent trial lawyer.

If you wander into Lincoln's papers ( and you can do that yourself, easily, through the Library of Congress site), you will constantly run across things you want to write down. I just went there and pulled up the first thing that popped into view. Here's an excerpt:

The desirable things which the individuals of a people can not do, or can not well do, for themselves, fall into two classes: those which have relation to wrongs, and those which have not. Each of these branch off into an infinite variety of subdivisions.

The first---that in relation to wrongs---embraces all crimes, misdemeanors, and non-performance of contracts. The other embraces all which, in its nature, and without wrong, requires combined action, as public roads and highways, public schools, charities, pauperism, orphanage, estates of the deceased, and the machinery of government itself.

From this it appears that if all men were just, there still would be some, though not so much, need of government.

Lincoln, A. (1840) Abraham Lincoln papers: Series 1. General Correspondence. -1916: Abraham Lincoln, 1840s Fragment on the "Legitimate Object of Government". [Manuscript/Mixed Material] Retrieved from the Library of Congress, https://www.loc.gov/item/mal0049400/.

The basic reason why you see so many good quotes by Lincoln online is, he wrote them.