I, as a DM, assume your character is trying the best they can at all times unless you say otherwise. Frankly, I think it would be pretty silly not to. Can you imagine failing a check because you didn't explicitly state that your character was giving it your all? Or having a character fail a roll, then ask to try it again with advantage because they're trying harder this time?
Why would a character ever give their best effort on a long jump if they know that best effort isn't needed? If the distance to be cleared is (e.g.) 5', why would a character instead try to jump 20'? A character is only ever going to try to maximize their jump distance if they think they have a need to jump that far. Saying that characters try to jump as far as possible whenever they jump just seems bizarre, not to mention also unnecessarily using up movement speed for the round.
If you give a DC every time they say "Hey, I just want to roll athletics to go farther," they will do so every single time they hit a jump that is longer than their base distance. That means that going farther isn't going to be unusual, it's going to be the norm. There's no reason not to try to jump further at every single distance that's longer than automatic.
Given the potential consequences of failure on jump checks (not infrequently including death for low-level characters), repeatedly trying to jump distances that require a successful check to clear is a self-limiting phenomenon. It can't become the norm because the character will roll too low at some point, and either won't be able to make future checks, or presumably will have a visceral reminder of why it's unwise.
Besides, why should it at all be surprising that characters who encounter a jump longer than they can clear with a auto-success may want to try it anyway? That's the entire point of ability checks: to model the resolution of tasks that have a chance of failure. To paraphrase: there's no reason (other than consequences of failure/opportunity cost) not to try to <insert ability check> at every single task that's too hard to permit an automatic success.
I think one of the things going on here is a fundamental misunderstanding of the jump rules. They are not how far you can jump easily. There may be no roll, but the very first thing that is said in the jump section is, "Your strength determines how far you can jump." Not how far you can easily jump. Not how far you can jump with no effort. Just how far you can jump, period. If you have an 18 strength, all of your effort will garner you 18 feet. If you want to go an unusually far distance, you need to use athletics to presumably, do something athletic like jump off of a rock, or jump and pull yourself further along by grabbing a stalactite.
I entirely disagree. Task resolution in 5e has three possibilities: auto-success, ability check, auto-failure. Usually the breakpoints are up to the DM, but in this case the jump rules specify that anything under a distance equal to your strength score is an automatic success. Anything beyond that is the realm of an ability check, both under the default rules and due to the inclusion of jumping longer distances as an explicit example of a Strength (Athletics) check.
Also, if your Strength score in feet was truly the maximum it was possible for your character to clear with a jump, the difficulty would be so high you'd need to roll a 20 to succeed, not so low that a DC doesn't even need to be set.
Unless failure = death/serious injury like when jumping, then you try as hard as you freaking can. Only a fool with a death wish is going to use only what they need and no more. It's easy to misread exactly how much you need and fall to your death.
If it's less than your Strength in feet there is zero danger of misreading how far you need--it's an auto-success! By definition, you only run into the problem of potentially failing because you misread the distance if the jump is far enough that the outcome is uncertain.