Even through it's possible, I don't think farther and son should have similar abilities. But farther and son have the same ability, in this case I think it's abnormal.
Aizen, Urahara, Isshin, all of them related to Ichigo in some way. After Isshin used Getstuga Tensho, I really believed that Isshin isn't Ichigo's farther. Ichigo isn't a human or shinigami, he may be a spacial type that made by them.
im thinking he might be a simillar to what aizen is now, which is someone who has a hougenkyo in him, but an earlier prototype and not as powerfull. its the only explanation i can come up with how chad and inoue got their powers after close contact to ichigo during a hallow altercation. it also fits into what ishin said that he couldnt sense aizen and only someone like him will be able to do so, and ichigo seems to be able to do that. he notices the abundance of reiatsu of aizen even though he's fighting with gin. maybe even taking it one step further, he was originally a hallow, got the hougenkyo in him, and wanted to be human more than anything. explains how ichigo got his hollow side.
in the last chapter mostly and just thought about it more. basically thats the first impression i got after reading page 3 then page 7. here have a look:
see after ishiin mentions he cant sense Ainzen's reiatsu and the only one who can is probably someone like him(Aizen), then on page 7 Ichigo turns his head and is shows that he does just that. i know he Ichigo could have done that due to the explosion, but i just got a different impression at first.
and just to add to my little hypothesis, the hougyonko or whatever inside ichigo doesnt react to desire, but rather to resolve. it fits on why he suddenly gets those power-ups all of those annoying times and nobody else has that kind of power.
The way Kubo writes his stories, it really wouldn't be too much a stretch to say that Urahara put a different hyogyoku inside Ichigo during his shinigami training.
The only thing that Kubo would have to explain (he would probably explain the same thing for 20 chapters) is why Aizen was saying things along the lines of him having something to do with Ichigo's birth.