You kinda always plan like that. If you do have a budget, you give a bit less money to a coach you aren't really certain about. I don't really feel that Rodgers could have influenced the Liverpool's board the same way Klopp did when going for Van Dijk and Alisson, the same thing is now happening there. Nuno was unproven and was given a chance to earn that 150 mil budget, whereas Conte is a proven winner with trophies behind him and the Spurs board will have more confidence in the players he will choose.
Yes, I agree with you. Conte and Nuno don't have the same profile. Conte is way higher profile than Nuno and thus he can more influence the board to give him more money. And also the board will be interested to do as Conte wants because they know that if they do so, Conte will have a higher chance of bringing success to them. So, I think that this is fairly normal.