Believe it or not, but the board shop will modify your artwork
they will modify widths and masks to meet the end criteria. that is part of their process. But i do not let them remove or add anything.
If the design violates one of their rules , or they find an issue they can tell me , i will fix the PCB and send new artwork. the board needs to match my cad 100%. I've been burned too many times with fixes done on the board that then were forgotten to be patched in cad and they ended up in the next revision. The CAD is the one true source of truth. I've also been burned with fabs adding copper balancing where this was not allowed ( Rf boards, boards with high voltage so their copper thieves basically shot the creepage to pieces. or stackups with other prepregs. I design the board. they make it. If they need to shrink the soldermask to compensate for bleed : fine, go ahead , but i call for 3 mils over copper with a max 2 mil misalignment. Class 3 boards.
And checking the gerbers not at all is just careless.
The board shop will find the issues if it doesn't match the netlist. What will you learn from the gerbers ? Besides , when i say gerber i really mean odb++ and more recently ipc2581. gerber is gone
Your layout tool might unintentionally obstruct some things. And having a different software interpreting the data as intended,
If the libraries are properly designed and the layout follows the rules all will be fine. If your libraries contains silscreen over pads and other shenanigans: fire your librarian.
As for other software interpreting data : that software too can have bugs. Gerber viewers are not cheap. Especially the ones that can do the front-end for the fab and the DFM. There's really only a few out there : Frontline Genesis , Ucamco or Lavenir ( Pentalogix) own that entire market.
I send my design through Valor before generating output as well.
Checking gerber is like checking that your postscript or PCL renders properly before you send it to the printer.
The gerber viewers do not add any value. The frontend processors do as they check against the fab design rules. But you can't do that as you do not have access to the "secret sauce" a fab uses. every fab has their own internal things they do to make your board. There are externally shared rules like track and gap and soldermask opening , but there is internal stuff that they do not share. If your design meets their external stuff there is a very good change it can be built.
Focus on making data that does not need corrections in the fab , like having to clip silkscreen becasue it is too close to other elements.
Also, check for assembly. your design should be solderable... Before you run the bare board : send the masks and padmasters to the assembler to verify for solderability. (or do this in-house using tools like Valor)