I think Tottenham's coach change is more important than strengthening the squad. Tottenham has never built a strong squad that can dominate the Premier League. That's why we have seen Tottenham's inconsistent performance in the Premier League every season. Since Tottenham's squad is not as strong as United, Chelsea or Arsenal, I cannot blame Tottenham's inconsistent performance only on the coach. Even if Tottenham management changes the coach, the new coach will have to provide a large fund to buy players. However, Tottenham management is not interested in spending a lot of money to buy players.
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The trick is, they are expecting someone to overachieve to be fair. Look at Villa, could you say that they were better than Spurs before Emery joined? Of course not, and after he joined the team he made every player better and right now Villa is easily overachieving what they should be doing.

But at the same time, we are seeing them not getting phased by the fact that they are doing great, I am sure they will consistently do better. There is a belief that if you switched the managers, Tottenham would be doing better and Villa would be doing worse than what they have done so far.

This is why I bet that Spurs changing the manager could do a lot, sure they would love to have some better players too, who wouldn't want better players, Real Madrid won la liga and UCL and still added Mbappe, if you can get better players then you get them but that's not the only thing, you need a better manager too, someone who doesn't just do what this team can do, that's not a success, if you make this team do whatever it can do then that's fine, but the reality is that if you can do better than what is expected then that's what you need as a manager.