Looking at two DTs drafted in comparable positions to where Settle is projected this year and or next. One of whom even stayed in school an extra year to bump himself to the first round.

Aaron Donald - 13th pick in 2014
Dalvin Tomlinson - 55th pick in 2017

Donald's rookie contract is 4 years for $10M
Tomlinson's rookie deal is 4 years for $4.5M

The franchise tag for the DT position in 2017 was ~$13M, a number that is exceedingly less than Donald is probably worth. I only say that because Settle thinks he's going to be a star and be in the league for a long time.

To reach that $13M number, a player has to play their rookie contract and an additional restricted free agent year depending on negotiations with the team. Now let's assume Settle isn't good enough to get tagged, but he will be a borderline top 15 DT in the league after 4 years. The yearly salary for the #15 DT (Damon Harrison) is $9.25M.

The difference over 4 years between a low teens 1st round pick and a late 2nd round pick is ~$5M, the difference between the salary of Donald's final year ($1.8M base) and the first year of the 15th highest paid DT is $7.45M.

TL:DR the difference in 4 years of salary between the 13th pick and 55th pick is less than the difference between the final rookie deal year and year 1 of the 2nd contract. So getting to the 2nd contract earlier, provided you're a successful player, is almost always worth leaving early for the 2nd/3rd round vs waiting a year for the 1st round contract.