The value of the player option to the organisation is that it meant David Price signed on the dotted line where he may well not have otherwise.
Every player option does not come with a team getting David Price. For example, when the Yankees gave CC a player option, they did not also get David Price. For the 4th (?) time, I was taking about the value of player options, not the value of getting David Price.
There's a separate discussion many have assumed is the same. It was pointed out earlier that player options might have more value to the player than they do cost to the team. Hypothetically, it might be worth $3m/year to Price to have the opt out but the Red Sox might only estimate this at the equivalent of adding $1M per year. So the Sox and Price should agree to discount the contract somewhere between $1M and $3M per year - everyone is better off. (This isn't the only scenario that could make sense. A player might refuse to sign with a certain team without one.)
Anytime this unequal valuing of the player option exists between a player and a team they player option should be included in the negotiation. Money is typically worth about the same to the team and the player ($1 is $1) but any time you have a negotiable chip worth a lot more to one party than the other, you should try and work it into the equation. Negotiations 101.
Tldr: even though player options are net negative to the team, they have a place in baseball if the team can extract discounts from the player to make it worth while. Hopefully this was the case with Price.
Regarding the value of player options in a vacuum, I have seen only two arguments on this board I buy as being logical arguments for them being a benefit to the team (meaning a team would offer a bigger contract to a player to include a player option or at least be indifferent):
1) For some reason teams can't trade a player mid contract (eg fan pressure/optics) so they include the option hoping that it will save them from themselves or from their fanbase. I find it dubious but it's definitely plausible
2) as motivation to perform well in the year(s) before the option treating it as a contract year. There's some truth to contract year improvement so I buy this but I think the value is probably mote as a function to create the unequal valuing between player and team I described above and not enough to turn player options into an actual positive for the team.
I think that player options are not in every contract is proof that teams don't view them as a net positive. They are inarguably a net positive for the player so if everyone thought they were awesome they would be standard.