There are many reasons why Isaac is considered the representative of the franchise.
One reason is the most simple. It is because he was the first protagonist that we controlled, and the one who started the series. First characters almost always get preference to be the series mascot. Also players were more likely to form an attachment to him rather than Felix who was first portrayed as an antagonist before he became playable in the second game.
Another more detailed reason is the whole arc that Isaac has throughout both games, that Felix lacks. Namely, the test that the Wise One made Isaac go through. Having initially lied to Isaac about the doom that the elemental lighthouses bring and sent him on a quest to prevent their lighting. With the Mars Star in tow, which would initially make no sense, but it was there since the Wise One's goal was to let Isaac find out the truth on his own (through Felix and co.) and to make his own judgement to light the last lighthouse with his former rivals. This ends up involving Felix as well at the top of Mars Lighthouse when they are forced to fight the Doom Dragon, who was actually the dragon form of Isaac's father and Felix's parents. The conclusion is at the top of Mt. Aleph, where it is revealed that the Wise One indeed chose to infuse the Mars Star with energy to divert the Mars part of the Golden Sun to Isaac, showing that he had indeed passed the test and had been entrusted with a portion of the Golden Sun's power. This act makes Isaac slightly more important than Felix even though Isaac was the deuteragonist in the second game, not the protagonist.
Third is Isaac's appearance in GS3 and his son being the protagonist. Camelot chose Isaac as the character to pass on the torch to his son to continue the series, rather than Felix being the older wiser character instead. Matthew also looks almost exactly like Isaac, except with a modern design, so he makes Isaac's face more iconic to the franchise again.
That's my reasoning anyway. Feel free to correct me if you think I got something wrong or missed something.
Edit: Adding what
@JaidynReiman said below, since Isaac got a part of the Golden Sun, Alex did not inherit that part. Which means that Alex has to go through Isaac to complete his goals of achieving power over all alchemy. So Isaac has a link to the main antagonist, making him the most important protagonist in the series.