Many of the cast having Starfleet parents doesn't surprise me, for the family tradition reason already mentioned.
However, is it really all that widespread? Leaving out ENT because of how early it takes place, it looks like TNG is really the only series in which a large portion of the main characters had Starfleet parents, and in DS9, the only senior staff member with a Starfleet parent was the crossover from TNG.
TOS: 1/7.
Kirk: Yes (father, Lt. Cmdr. George Kirk).
Spock: No (and his father actively disapproved).
McCoy: Unknown.
Scotty: Unknown.
Sulu: Unknown.
Uhura: Unknown.
Chekov: Unknown.
TNG: 4.5/9.
Picard: No.
Riker: Sort of (Kyle Riker was a civilian contractor with Starfleet, so let's call him a half for the purposes of the ratio).
Data: No.
LaForge: Yes (both parents: Cmdr. Edward LaForge and Capt. Silva LaForge).
Worf: Yes (adoptive father: CPO Sergey Rozhenko).
Troi: Yes (father: Lt. Ian Troi).
Beverly Crusher: Unknown.
Wesley Crusher: Yes (both parents: Cmdr. Beverly Crusher and Lt. Cmdr. Jack Crusher).
Yar: No.
DS9: 1/6.
Sisko: No.
Jadzia Dax: No.
Ezri Dax: No.
O'Brien: No.
Bashir: No.
Worf: Yes (see above).
(Leaving out Kira and Odo, since they're not in Starfleet either.)
VOY: 2/6.
Janeway: Yes (father: Admiral Janeway).
Chakotay: No.
Tuvok: Unknown (though he did join at their behest).
Paris: Yes (father: Admiral Owen Paris).
Torres: No.
Kim: No.
(Leaving out Neelix, Kes, Seven and the Doctor; including Chakotay and Torres because both were inducted into Starfleet by Janeway and had a prior Starfleet background.)
However, is it really all that widespread? Leaving out ENT because of how early it takes place, it looks like TNG is really the only series in which a large portion of the main characters had Starfleet parents, and in DS9, the only senior staff member with a Starfleet parent was the crossover from TNG.
TOS: 1/7.
Kirk: Yes (father, Lt. Cmdr. George Kirk).
Spock: No (and his father actively disapproved).
McCoy: Unknown.
Scotty: Unknown.
Sulu: Unknown.
Uhura: Unknown.
Chekov: Unknown.
TNG: 4.5/9.
Picard: No.
Riker: Sort of (Kyle Riker was a civilian contractor with Starfleet, so let's call him a half for the purposes of the ratio).
Data: No.
LaForge: Yes (both parents: Cmdr. Edward LaForge and Capt. Silva LaForge).
Worf: Yes (adoptive father: CPO Sergey Rozhenko).
Troi: Yes (father: Lt. Ian Troi).
Beverly Crusher: Unknown.
Wesley Crusher: Yes (both parents: Cmdr. Beverly Crusher and Lt. Cmdr. Jack Crusher).
Yar: No.
DS9: 1/6.
Sisko: No.
Jadzia Dax: No.
Ezri Dax: No.
O'Brien: No.
Bashir: No.
Worf: Yes (see above).
(Leaving out Kira and Odo, since they're not in Starfleet either.)
VOY: 2/6.
Janeway: Yes (father: Admiral Janeway).
Chakotay: No.
Tuvok: Unknown (though he did join at their behest).
Paris: Yes (father: Admiral Owen Paris).
Torres: No.
Kim: No.
(Leaving out Neelix, Kes, Seven and the Doctor; including Chakotay and Torres because both were inducted into Starfleet by Janeway and had a prior Starfleet background.)