Ross Barnes (1850-1915) was the most dominant player in the short-lived National Association. In his 9 seasons between the NA and National League, he led the league in batting average 3 times, had an OPS over 1.000 4 times, and had an OPS+ 200 or more 3 times. Additionally, his glove was better than most in a era without gloves or modern understanding of defense. Though a .876 fielding percentage would be a worse second base than Dan Uggla on his worst day, this was about 40 points higher than the average second baseman over his career, and he had a range factor per 9 of about .6 higher than his competition.
But Barnes, despite being the most dominant player in the NA, is not in the hall of fame for a few reasons. One, his career was severely shortened by a nameless illness that made him only able to compete about 180 games for the last 5 years of his career (1877 to 1881). Even when he was able to play, he did not do so well.
Second, the short seasons of the NA resulted in his career counting stats being underwhelming to the rest of the players in the hall of fame. In his peak, Barnes could only play in about 45 to 80 games a year. His 27.7 bWAR is lower than players like Marquis Grissom, Martin Prado, and Terry Puhl. He accumulated under 900 career hits and under 1200 total bases (he had fewer total bases than Mark Reynolds if you only count his home runs, nevermind the rest of his hits). However, his rate stats are among the best of all time. Barnes has the highest runs scores per game (almost 2 per game), had a .360 career average (which would be 2nd all time if he qualified), and his WAR is actually very high if adjusted to 162 game seasons. In the National Association and his first year in the national league, if adjusted to 162 games each year, these are his seasonal bWAR totals: 11, 15.5, 13.2, 7.6, 10.8 and 14.7. Of course, there are several asterisks here, including that Barnes doesn't seem like he was particularly durable at any point in his career and so would be unlikely to play 162 games in a season, the fact that this may be more a failure of the calculation of WAR trying to evenly compare players among all eras with one stat (this is also glaring with 19th century pitchers having seasons approaching 20 WAR a season with 40 fewer games a season) among other issues.
Lastly, Barnes did not play 10 career years, the number needed to have consideration to be inducted into the hall of fame.
Barnes may have been one of baseball's first stars, but while the 1880s and 90s was defined by Cap Anson, the 1900s and 10s to Cobb, the 20s belonged to Ruth, and so on, Barnes illness and the limitations of early baseball held him back from the same glory.