I know for those following along with the Podcasted The Starter that the Krakens signed a few players from tier two at the beginning of the season, but few teams with contracted players would want their players risking injury in the off season.
The major barrier to a pure relegation system in major league baseball is the farm system and the game itself.
Baseball may be able to have cactus league play in arizona during the winter, but do you really feel like putting out your pitcher in a frigid 20 below in the middle of Montana or Minnesota. Short of domes which are cost prohibitive to the minor leagues all the new teams entering the league would be from the south. The less likely chapions would be dome / snowball teams(cold weather specialized). Imagine going to a championship game in February for the right to go to tier one with an icy field and snow falling as you sit there and shiver not very healthy for the most risky position in the game the pitcher.
Second, apart from minor league teams that are in other leagues, minor league baseball is a farm system for the majors. They play at the same time so players that are struggling or coming back from injury can come back at a lower level until they are back to form. Most players at this level are under contract allready with MLB teams.
Imagine if a major league team had their affiliate minor league team move to tier one. That would be devastating. It would lead to teams having multiple tier 2 affiliates or pushing their affiliate to throw games so they can keep serving their real purpose of physical therapy and confidence booster not winning.
MLB is a club that you can't join unless they approve you. Even if I had a trillion dollars if the owners didn't aprove me I could not buy a Team. Rush Limbaugh wanted to buy in as part owner of an NFL team, but he was not allowed due to his controvercial comments about Michael Vick (which at the time turned out to be correct that year) MLB works the same way.
Do you really think that whoever could win a tier two championship would be welcomed at the next Tier one owners meeting. They would either have to invest in a tier one quality facility for their minor league team or would be playing Tier One ball in a Tier Two stadium. Do you really think MLB would agree to allowing the possibility of a major tv market losing a team due to a bad year, or a nowhere town like Green Bay Wisconsin or flint Michigan to get a team in the current day?
What about a competing team in the same city (What if Chicago or NY had a third team rise out of tier two which league do you put it in? If they had a deal as a minor league team to use the same stadium as a major league team and they played eachother who would have home field advantage? Would it be an artifical away game for one of the two teams?
The value of a franchise would drop if a relegation system was implemented. If there was simply an 8 team relegation league that was still major league baseball there could still be an approval system, and there could still be many of the advantages of these teams having an easier schedule while they are rebuilding. Also allowing for a less painful entrance or exit of a team from the league.
I think the variation of Relegation suggested on the radio is superior given the current state of MLB. Though if you ask me they need fewer teams and shorter seasons so that the best players are playing every game.