Arsenal has two strikers available, Havertz and Gabriel. They don't mind adding a new striker. They think those two names are enough to help them this season. They are focusing on other positions, not the striker position. They scored a lot last season. It's probably their reason to feel confident enough with their available strikers. And they decided not to sign a new striker.
I also think that it's not a problem for Arsenal when they don't recruit a new striker, although it wouldn't be wrong if Arsenal wanted to recruit another new striker to replace one of them if they get injured during the season. However, the reason you said could also be very logical because Arsenal also thinks more about other more important lines such as the midfield and defense so that the opposing team will not easily break into their goal when competing in any competition.
Arsenal put up a great performance against Manchester City. Of course, it would be logical for them to want to replace injured players, but Arsenal seem to be fully prepared at the moment. They have not been defeated in the league yet and drew with a goal they conceded in the last minutes against Manchester City. They were going to beat Manchester City. This shows us how well they played. Arsenal is a dangerous team this year. They will continue to be competitive in the Premier League until the end of the year. They can also be one of the teams close to the final in the Champions League, as long as things go well. Their squad is suitable for this.