I don't think not signing another centre back in the summer is the issue. Zimmermann is our captain and runner-up in the player of the season vote, and Godfrey is England under 21s captain and was superb during the 2nd half of last season. With Klose as back-up who was also very good when he played last year, and if need be Hanley who was one of our best players in Farke's first season, as well as Amadou as emergency cover, that's more than enough options, and I don't think we could've signed anyone who is an upgrade on Godfrey or Zimmermann. Like Morty said you can't just sign an overload of players for each position on the off chance you have the worst injury crisis in the history of the club. On paper our defence coming into this season was more than good enough. Also, I don't know where the idea that Byram can play centre back has come from. Obviously I haven't watched him his whole career, but nothing about him and the way he plays suggests he can fill in there. I imagine if need be Farke would sooner move Lewis into the centre and play Byram at left back.
We conceded a lot of goals last season because of the way we played, not the personnel. We concede a fair amount, but scored more, like we did under Lambert. The problem isn't that we're letting a lot of goals in, because we did that last year and still won the league. The issue is we're not scoring goals. Brighton on Saturday is the perfect example. They didn't score their first goal until the 70th minute, if our attack is on song we score the first goal well before then and it's a completely different game. I don't want to 100% blame the injuries, but it's impossible to overlook the disruption it would've caused to the squad. The constant swapping and changing in midfield means we just haven't been able to get any consistency or balance in that area all season, which has massively impacted how good our attack has been. Add to that Patrick Roberts, who was our main signing in attacking midfield and is probably someone Farke had big plans for this season, is essentially ruling himself out of contention (I said before but basically someone reliable told me Farke does not like his attitude at all, hence why he doesn't feature). While we put in work to make sure the players we sign have an attitude and work ethic that will fit in at the club, that sort of thing is hard to determine until the player actually signs. If instead of him we sign an attacking midfielder who actually wants to be here then maybe they could be a key part of our attack and help us to get the goals we need (and tbh I hope in January if Roberts still hasn't shown enough we send him back to City and sign someone to replace him).
We have been dire away from in particular this season, there's no arguing with that and injuries or not we should be doing better. But I'm still confident that when we get the likes of Zimmermann and Vrancic back, and hopefully have a full-strength team, consistent team for a few games that we will start getting results.