With good supports you can hit pretty high numbers.

"Professional" parsers do a parse setup with food, pots, etc. It does not translate 100% over to live action. You will run different food, have to mitigate damage, do mechanics, keep a rotation that will get interrupted, and with the newer trials, focus different adds while avoiding damage from environmental or other sources. At the same time, you will have more group damage and sustain from synergies and support sets. In the end, if your actual damage is within 85% of your parse, you're fine.

parsing helps with refining/practicing your combat rotation

you need "live" combat in order to practice doing your rotation while also under fire

theres a few different ways to practice though

"solo" practice, which is mostly good for arenas
"group" practice, essentially doing group dungeons, or at least having 1 tank/healer (can be the same player or 2 different players) with you to more easily simulate in a group

as a dps, in a trial group you can have a self heal as a kind of backup for if you need to run away from the healers (doing mechanics or something), but generally should be able to rely on healers for the majority of staying alive as long as you can position correctly

as noted by others in this thread, it also does vary a lot depending on the boss if you can just "parse" on it

yolnakriin from sunspire is a good example of a "parse" boss for the most part, its mostly stack and burn, vrol and yandir in kynes are also kind of just sit there and parse and occasionally turn and burn something else

The role of support can make a massive difference in the numbers you hit - thats why most end game guilds ask for a log in addition to a parse, since it says way more about your performance.

Parsing is a great help to understand a build and train your Priorities/Rotation as a DD. The better you know that, the more time you have to concentrate on mechanics and positioning during a fight.

comparing your own parses to see progress and comparing with other parses to find out what you might do wrong, like

do i have the same skills in my top damage like a pro parser
how often do they use a specific skill (some are for example only in the bar for buffs and not used at all)
and so on

So parsing is a very good way to show single target damage potential of a build - thats why they use it to advertise their builds - real combat is a different story but not a totally different one.