Most newspapers just use hobby photographers who are happy to be there, often they are new to photography so they are a happy to give their work for free and happy to see their name credited.
A newspaper would rather use a 3 out of 10 shot for free than a 9 out of 10 shot that costs money. Hobby photographers usually get fed up when their camera breaks and can't pay the repair with the money they have made from photography.
A newspaper should apply for you after all they are getting free images. It's pretty easy to get into 95% of sporting events using a local paper or agency that will give you a % per sale.
The last line there is critical as well. To really build out an impressive portfolio, you need impressive content. To get access to shoot that content, you need credentials quit often. A media pass is something of value to someone building their skills or body of work. For example I see too often people who have done youth sports, and have fine work, not be able to provide any tear sheers when asked in the process of trying to get "paid" work. To have extrodianary work, you need extraordinary access, and you need to get published. In formal channels that called interning. In less formal, that is access for prints.
Too many who don't know the business don't understand that in the early stages, pro bono and quid pro quo work is part of the process to built a portfolio of work. Models do it. Fashion Photographers do it. And sports photographers do it.
