If the VA only treats service connected Veterans, then they would have to close a good number of VA Medical facilities (hospitals and clinics) due to the rapidly shrinking and aging Veteran population (28.5 million in 1980 to roughly 19.3 million in 2014). Roughly half the 19.3 million Veterans are over 65.
Veteran Population Census data 1980-2000
In 2014, there was roughly 3.8 million Service Connected Veterans with ratings ranging from 0% to 100% (1.1 million rated at 70% or higher). In FY 2014, 9.1'million Veterans were enrolled in VA healthcare and 5.9 million used VA Healthcare during FY 2014.
Number of Veterans using VA healthcare
You can't justify keeping the VA healthcare system at its present size if you limit access to Service Connected Veterans only. That is why they are permitting many (not all) non-service connected Veterans to get VA healthcare. With the rapidly shrinking Veteran population, they either have to see more Veteran patients or start closing many VA facilities, further restricting access for Veterans to VA Healthcare