"if Alekhine is champion till his death because he was undefeated, shouldn't the same be true for Fischer"
Obviously not, do you think Fischer could stay World Champion for 36 years simply by not playing and make it impossible for players like Karpov and Kasparov to ever play for the World Championship during their careers?
Yes, that was system which was followed until Alekhine died with Championship. Then the new system was developed and Fischer became the champion. He didn't play Karpov because his rules were not agreed to. So, Fischer was the undefeated champion even if Karpov was promoted by FIDE.
"if Alekhine is champion till his death because he was undefeated, shouldn't the same be true for Fischer"
Obviously not, do you think Fischer could stay World Champion for 36 years simply by not playing and make it impossible for players like Karpov and Kasparov to ever play for the World Championship during their careers?