There were probably several players that needed to be replaced the previous year.
The out-of-universe explanation is that, yes, having the same batch of players in the team throughout Harry's first few years gives consistency and stability. We aren't being constantly introduced to new characters unnecessarily.
From an in-universe point-of-view, there are three principles of Gryffindor's team selection to bear in mind.
Team members were appointed on merit, regardless of age.
"At least no one on the Gryffindor team had to buy their way in," said Hermione sharply. "They got in on pure talent."
(Chamber of Secrets, Chapter 7, Mudbloods and Murmurs).
Younger players from lower years are certainly not unheard of.
Remember that Malfoy managed to get into the Slytherin team in his second year (albeit using bribery). When Harry came to picking his own team, he showed that he wasn't averse to picking players from lower years.
Neither of his chosen Beaters had the old brilliance of Fred and George, but he was still reasonably pleased with them: Jimmy Peakes, a short but broad-chested third-year who had managed to raise a lump the size of an egg on the back of Harry's head with a ferociously hit Bludger, and Richie Coote, who looked weedy but aimed well.
(Half-Blood Prince, Chapter 11, Hermione's Helping Hand).
First-years never play in the teams, apart from Harry.
"Seeker?" he said. "But first-years never - you must be the youngest house player in about -"
"- a century," said Harry, shovelling pie into his mouth. He felt particularly hungry after the excitement of the afternoon. "Wood told me."
(Philosopher's Stone, Chapter 9, The Midnight Duel).
The most likely explanation for Gryffindor's young team in Philosopher's Stone was that a spate of players had left within the previous year. It might be helpful to lay out all the known Gryffindor Quidditch players over the six years that Harry is at Hogwarts, with the year each player was in when they joined the team:
Permanent players:
Oliver Wood (Keeper, 5th year in PS)
Alicia Spinnet (Chaser, 3rd year in PS)
Angelina Johnson (Chaser, 3rd year in PS)
Katie Bell (Chaser, 2nd year in PS)
Fred Weasley (Beater, 3rd year in PS)
George Weasley (Beater, 3rd year in PS)
Harry Potter (Seeker, 1st year in PS)
Ron Weasley (Keeper, 5th year in OotP)
Demelza Robins (Chaser, year unknown in HBP)
Ginny Weasley (Chaser, 5th year in HBP)
Jimmy Peakes (Beater, 3rd year in HBP)
Ritchie Coote (Beater, year unknown in HBP)
Temporary players:
Unknown player (Seeker, year unknown in PS)
Ginny Weasley (Seeker, 4th year in OotP)
Jack Sloper (Beater, year unknown in OotP)
Andrew Kirke (Beater, year unknown in OotP)
Dean Thomas (Chaser, 6th year in HBP)
Cormac McLaggen (Keeper, 7th year in HBP)
We can tell which year people are in based on when they leave Hogwarts, or if it's directly mentioned in the books (in the case of people like Peakes). I've seen some sources online which say that Robins was in her fourth year but I haven't seen any evidence for this from the books.
Anyway, it's plain enough that Gryffindor kept the same team together throughout Harry's first four years. Nobody was replaced because nobody had left. Even in his fifth year, the only player that needed to be replaced was Wood. However, during Half-Blood Prince a total of four players had left or graduated, meaning that wholesale replacements were needed.
The same sort of situation seems to have arose either during Philosopher's Stone or, more likely, the year before. Spinnet, Johnson and the Weasley twins were all in the same year but seemed to be fairly well bedded in during PS. They seemingly all knew one another well having played together the previous year as a bunch of second-years. We know that Spinnet wasn't in the first-team that year but did feature as a reserve (which may well include training with the team and so on):
"And she's really belting along up there, a neat pass to Alicia Spinnet, a good find of Oliver Wood's, last year only a reserve - back to Johnston...
(Philosopher's Stone, Chapter 11, Quidditch).
We know that the Weasley twins at least had already been in the team for a year.
"We know Oliver's speech by heart," Fred told Harry. "We were in the team last year."
(Philosopher's Stone, Chapter 11, Quidditch).
It's debatable who Fred is talking about here. By "we" he could mean just him and George. Or he could be referring to Angelina as well. Either way, I think it's likely (if not proveable) that all of them were in the team.
The next year (Harry's first) Wood had three places to fill: two Chaser slots and the Seeker. (We know that Charlie Weasley was the old Seeker and had left Hogwarts the previous year). Wood appointed Katie Bell, a second-year, as a new Chaser at the Quidditch trials at the start of PS, which as readers we never get to see. Alicia Spinnet was promoted from the reserves. As NKCampbell demonstrates, he had already appointed Harry, a first-year, prior to the trials taking place. It's clear that he wasn't planning on picking anyone that young but did so on McGonagall's personal recommendation.
So it was partly by chance that Wood ended up with such a young team. Indeed, he was probably the only player who'd played more than one full season come the start of Philosopher's Stone. However, he appointed the majority of his team from trials and happened to pick second-year students in each case.
There are a variety of reasons why Wood may have picked a younger team, some of which are laid out on this Reddit thread:
It may have been that, coincidentally, the best players just happened to be the younger ones.
It could be that older players didn't want to apply, to focus on studying, because they were part of other clubs or for some other reason.
Wood may have judged that picking young players would allow the team to bond together over time. By gradually getting to know one another's strengths and weaknesses, the players would be better able to play as an effective unit. This proves to be a shrewd move as, after playing together for three years, the Gryffindor team is a force to be reckoned with in Prisoner of Azkaban.
Wood may have felt intimidated by older students. He was the captain but he was only in his fifth year. He may have felt that it would be easier to manage players who were younger than himself.
