Well, I'm trying to look at it from both sides to be honest.
In favor of trading for Pap, Tazawa has not looked all that great lately, and has no closing experience, and he's really only been on a competitive team and throwing meaningful innings for 3 months, so how he reacts to a big game blown save is very much unknown, Uehara can't pitch in back to back games outside of only every once in a while, and RDLR is having some command issues in Pawtucket. Yes, it's going to cost prospects but if you're going to trade for a RP, Papelbon is a very well known commodity, he has had success in Boston, and has won a World Series so you know the pressure is not going to get to him. His K/9 is down but he's still got an 8:1 K:BB ratio which is more than enough to be an effective closer, he's not had any injury concerns, and he is having a lot of success in Philly, which is a market a lot like Boston.
In favor of looking internally, closers can appear out of no where, meaning players rarely come out of the minors and close. Most of the time it's a conversion from a very strong relief ace situation, much like Tazawa is now. RDLR clearly had the stuff to be a closer and it's well documented that control and command issues have significant correction when moving from a starters role into a relief role, and K rates increase as well (see: Andrew Miller), so just because RDLR is having those command issues from a starters role doesn't mean they won't be corrected in a relievers role (again, see Daniel Bard minor league conversion). Also, Jason Motte and Sergio Romo had little to no closer experience before their respective teams won the World Series over the past 2 seasons.
So, the question is whether you go with a reliable guy like Pap and know what you have or you roll the dice, hope one of your options catches a little lightening in a bottle a la Romo, and you are ok.
Personally, I would like to see the Sox give Taz and RDLR a couple opportunities to close out some games between now and mid July to see exactly what are options are. The worst thing would to go into the deadline blind about your depth options because you were trying to build Baileys confidence, the same Bailey who you demoted in the offseason for Hanrahan.