It really depends on the player but unless you're drastically overpaying said asset, most teams will gladly match and then that's that.
$500k more for Bouchard isn't all that much more. Broberg is probably making more than double what he's worth. If the Blues offer sheeted him for less than 3m the Oilers probably would've matched already without much discussion.
The reason that GM’s don’t typically offer sheet each others rfa’s is because collectively they don’t want to give player agents negotiating leverage for younger players who are still unknown quantities which would drive up the cost and risk for everyone when signing players out of elc’s. If it became open season on rfa’s then it also provides another avenue for players to force their way off teams.
Consider this situation. A top 10 pick is playing for a bad team that doesn’t have a lot of talent in the lineup. He refuses to sign with his team before July 1 at which point his agent goes on the hunt for offer sheets. A team like Edmonton comes along and offers a contract like what STL did and the chance to play with mcdavid/draisaitl, making it as uncomfortable as possible for the players current team for the least amount of compensation.
The player signs the offer sheet and tells his current team he doesn’t want to play there but of course they have the right to match the offer. So what do you do at that point? You’re a rebuilding team that spent a top 10 pick on this player and invested 3 years of development time into him and now your options are severely over pay for a player you’re still unsure about and who doesn’t want to be on your team or take a late 2nd rounder for him?