Just think about hardwood floors verses your dining room table. If it has a quality finish you will be ok.

I think there would be more scratches w/o tablecloth than with tablecloth. Depends on how long you want to keep your table as young families wear things out sooner than not. Personally I don't use a tablecloth b/c I want to show off the beautiful wood, but I also don't have a family eating or playing there daily.

Always use padding underneath when homework is being done. The pressure from writing will make indentations in the surface.

Oak is a hard wood; some other types of wood may not do as well; my dining table has indentations on it where my roommate used it for a writing surface. They are not obvious but can be seen when looking for them however all my furniture is slightly distressed just for that reason

The only wood that would dent like that would be pine....or perhaps a cheap something meant to be stained to look like something else....one ole timer I know called it "tree wood"...LOL! I have a friend who bought a beautiful old pine table that had been used to roll dough, prep foods etc.....but never written on with a ball point ben.....and it has a record of every letter, list made and check written!
But as I said.....what are you saving it for? Enjoy the wood and if it gets marks from writing on it....THEN cover it with a cloth.
But you know what? My family has always observed care of nice furniture ( outside of the nail polish incident!) and we make it a habit of writing on a pad rather than a single sheet of paper and always using a coaster under your glass. We put our feet on the coffee table in the family room but remove our shoes first, and don't worry about candle drips because we know those are easily removed.

That is the key is using a pad rather than a single sheet of paper; it prevents the pressure of the pen or pencil making the indentations in the wood. My table is by Kincaid who makes a decent product, solid wood but was used to write on by a friend whom I assume did not know better.

Yeah....solid wood...but what kind of wood? Ball point pen in some hands can be a formidable tool!

When the kids built stuff with legos or colored with crayons, I didn't worry about the table, but when the play-do came out, or something involving glue I told them to please work on some newspaper. Then when they were through, I could roll up the whole mess and toss it.
Milk and cookies were eaten at the table, but we always use place mats for a meal and trivet or hot pad for a hot dish.
As I said, there's no reason to cover up your table, but use reasonable care on a daily basis and you will enjoy it for years....without hiding it under a cloth. I have a friend who always had her kitchen table, where the family ate and the kids did homework and crafts, covered with a cloth. I thought that odd but one time when I was there she changed the cloth and I saw why she kept the table covered. Don't hide a pretty table, cover an ugly one.