This is not a simple question but let me break down the factors surrounding this decision.
1) Fnatic have always expressed their desire to play with Rekkles When Puszu joined the team it was agreed that Rekkles would replace him in S4 by all relevant parties. You have to remember that if they could've, Fnatic would've taken Rekkles to worlds instead of Puszu. Age law and date of games fucked them over and they decided that going all tournament with Puszu was a better call since changing player mid tournament is kind of rough. Rekkles lives with Fnatic, is on salary with Fnatic and streams under the Fnatic network. Also Yellowstar duoqueues a lot with Rekkles, far more than he ever did with Puszu.
Also funfact that after Lamia retired Fnatic had 3 main candidates for the spot of ADC on their team. Rekkles, CandyPanda and Yellowstar and despite the tremendous experience of CandyPanda and Yellowstar Fnatic went with Rekkles because they saw something in him as a player.
2) "Puszu deserves his place in Fnatic" That's not the way it works sadly. If you have a better player available and a whole year to work on synergy it would be a disservice to the players and the fans to not go with them. Korean teams are renowned for (and fall under criticism when they don't) bringing in new talent as soon as possible. Look at Ssong from Sword or Homme from Ozone, willingly giving up their spot at Worlds for the sake of the team and the potential of new talent in Nagne or Looper. Sure this doesn't always work out but if you have a whole year to work on teamwork and develop a player then the likelihood of it blowing up in your face is lowered significantly. Competitive League of Legends isn't a holiday, players are expected to make the appropriate and tough decisions in order to maintain as competitive and strong as possible.
Benching Shusei in favour of sOAZ was an unpopular decision and sOAZ later emerged as the best European toplaner and the only one impressing on a world stage. Benching nRated in favour of Yellowstar was another unpopular decision that again worked out very well for Fnatic given how quickly Yellowstar became a world class support player.
3) Puszu played really well Did he? I mean, he was losing bot lane really badly 4 games in a row. Homme played well in Champions Spring and Summer, Ssong played OK in Spring and the whole team played poorly in Summer, didn't stop them stepping to one side for younger talent. He wasn't the only thing under-performing, xPeke did that as well. But last time I checked Fnatic don't have a young superstar prodigy of a midlaner with a huge fan following sitting on the bench.
4) What has Rekkles done that's that impressive? He's done everything he can. Since leaving Fnatic he built up a sizeable following, joined an amateur team and competed in amateur tournaments winning a good amount of them. He plays really, really well for CW and consistently carries nearly every game (and if he doesn't then CW lose). Like Uzi was in this series; Rekkles is always up on CS, sometimes even over 100 cs. Since stepping down Rekkles has improved his positioning, map awareness and skillshot aim drastically but maintained his flashy mechanics. He's also improved his champion pool drastically (since before he could only really play Ezreal at a top level). I've seen him play Tristana, Caitlyn, Twitch, Varus, Ezreal, Corki and Vayne all at a very high level. Also anyone who knows Rekkles will know that he practices a lot, as much as any of the other Fnatic players do.
5) Rekkles fits the Fnatic brand. Fnatic have a reputation for strong individual play. Ask any EU LCS fan who the best toplaner, midlaner and jungler are in Europe and it's highly likely that sOAZ, xPeke and Cyanide will get a mention in their top 2/3 (got to allow for fan favourites). When you say strong EU ADCs (what an oxymoron of a sentence) for like their dream-team or some shit most people would say Lemondogs Tabzz, NiP Freeze SK CandyPanda and ATN Creaton. Rekkles is the kind of player who could be on the top of everyone's list, he was last year in the aftermath of IPL5.
6) If they don't commit to Rekkles in the next few weeks some other team will SK perhaps need a new ADC (they're trying out MrRallez at the moment), Copenhagan Wolves want an ADC to qualify with and even teams like Evil Geniuses may consider picking him up. Rekkles is held in very high regard amongst high elo and pro players and he has other offers, I know that much at least.
Fnatic have nothing to lose and everything to gain. Also remember they can do an intensive scrim session with Rekkles and try him out for the role before committing.
Finally a superstar EU ADC, we haven't had any ever. Creaton seemed like he could've been the one at the beginning of the summer LCS, but otherwise all mediocre. Good ones I would say Freeze, Creaton that come to mind.
I gotta go with what people have said. Puszu is an excellent ADC in his own right and gave Fnatic a strong botlane, but Rekkles is who they've been planning to go with all along. It's not like Puszu is going to struggle to find a team as he's already proven himself, and if he stays with the Fnatic organization then they know they have someone they can rely on to back them up. Should Rekkles not work out and he stays with them, then that shouldn't be a problem.
Puszu has done amazing for fanatic this last year, but the plan was always to get reckles when he was old enough, he will without a doubt find a new team very quickly, such a good player wont go to waste, there was talk about cw wanting to pick him up if he was willing.