I went looking for the rules. Maybe it is the football HOF that has limited fan participation. Here are the Baseball HOF rules (from here).


Rules for Election to the National Baseball Hall of Fame by Members of the Baseball Writers' Association of America (BBWAA)

1. Authorization — By authorization of the Board of Directors of the National Baseball Hall of Fame and Museum, Inc., the Baseball Writers' Association of America (BBWAA) is authorized to hold an election every year for the purpose of electing members to the National Baseball Hall of Fame from the ranks of retired baseball players.

2. Electors — Only active and honorary members of the Baseball Writers' Association of America, who have been active baseball writers for at least ten (10) years, shall be eligible to vote. They must have been active as baseball writers and members of the Association for a period beginning at least ten (10) years prior to the date of election in which they are voting.

3. Eligible Candidates — Candidates to be eligible must meet the following requirements:

A baseball player must have been active as a player in the Major Leagues at some time during a period beginning twenty (20) years before and ending five (5) years prior to election.
Player must have played in each of ten (10) Major League championship seasons, some part of which must have been within the period described in 3 (A).
Player shall have ceased to be an active player in the Major Leagues at least five (5) calendar years preceding the election but may be otherwise connected with baseball.
In case of the death of an active player or a player who has been retired for less than five (5) full years, a candidate who is otherwise eligible shall be eligible in the next regular election held at least six (6) months after the date of death or after the end of the five (5) year period, whichever occurs first.
Any player on Baseball's ineligible list shall not be an eligible candidate.

4. Method of Election

BBWAA Screening Committee — A Screening Committee consisting of baseball writers will be appointed by the BBWAA. This Screening Committee shall consist of six members, with two members to be elected at each Annual Meeting for a three-year term. The duty of the Screening Committee shall be to prepare a ballot listing in alphabetical order eligible candidates who (1) received a vote on a minimum of five percent (5%) of the ballots cast in the preceding election or (2) are eligible for the first time and are nominated by any two of the six members of the BBWAA Screening Committee.
An elector will vote for no more than ten (10) eligible candidates deemed worthy of election. Write-in votes are not permitted.
Any candidate receiving votes on seventy-five percent (75%) of the ballots cast shall be elected to membership in the National Baseball Hall of Fame.

5. Voting — Voting shall be based upon the player's record, playing ability, integrity, sportsmanship, character, and contributions to the team(s) on which the player played.

6. Automatic Elections — No automatic elections based on performances such as a batting average of .400 or more for one (1) year, pitching a perfect game or similar outstanding achievement shall be permitted.