Yes, you can push cap hits into future years by renegotiating - but that pushes the cap hit into future years, and may lock the team into players they would rather cut, because the cap hit would be too large.
There may also be a limited number of players on a team that it makes sense to renegotiate.
For instance, if a player has one year left on their contract, is needed for next year, but is old enough the team doesn't want to commit to a year or more beyond that, renegotiation does not make sense. Or maybe the player is already expensive, and renegotiating to save cap money this year means that he will be very expensive next year, with a big dead cap hit if he's cut thanks to the renegotiation. GMs have to factor in what a signing will do to every year affected.
The biggest cap hit at the moment is Andrew Whitworth. His cap hit for 2018 could be reduced by $3.5 million by converting $7 million of his 2018 salary to a signing bonus. Of course, that means that in 2019 at age 38 he will have a cap hit well north of $15 million, with over $5 million of dead cap, either of which would put the Rams into a bad cap situation. Money could also be saved on Barron - but again, that would make his cap hit bigger in future years and the dead cap correspondingly more painful, while the Rams would be trying to pay for AD, Gurley, Goff, Cooks, etc.
In theory the cap can be adjusted to save money for year one - but at a cost that actual GMs quite often are unwilling to pay, since they are paid to think about more than year one. These are Ram examples, but every team has something similar.