Remember that Geas and Quest are level 6 spells, with no saving throw, and with a casting time of only 10 minutes, plus the subject takes 3d6 damage (and becomes sickened) every day he doesn't try to accomplish his quest.
Having a Permanencied Love Letter (at a cost of 3,000 xp to the caster) seems interesting and fun, rather than game breaking.
As it currently stands, there is absolutely no reason a caster would choose to use Love Letter instead of Lesser Geas or Geas.
The only potential advantage I see to your Love Letter spell is that you can deliver it via the mail, rather than by wiggling your fingers at someone. Of course, that has downsides. A servant or courier could read the letter before delivering it to your intended target. Also realize that once a person has read this Love Letter, they are going to put it in their pouch/pocket to keep it close to them as they search for their onetruelove. The letter will almost never be read by more than one person, thereby negating one of your potential "pros" and moving it to the "cons" column.
Stalkers in love are creepy, bro.