My current porch is like this
The columns are rotting and the deck was poorly built, posts aren't directly under columns and most are just on dirt.
I intend on doing a rebuild. With the columns I was considering replacing them by 6x6s and running them all the way to ground level on top of a footer instead of having the column on top of a the deck over a post. A similar example is here
Is this a bad idea?
The columns and supporting posts have different jobs, so for design, cost and aesthetic reasons it often makes sense to place them separately.
You may want the columns to be placed in a way that visually aligns with the first or second floor or with the stairs, but the posts to be placed in a way that is more coupled to the framing or footing layout, neither of which have to visually make sense.
You may want the columns to be ornate, like yours. It's harder if not impossible to find ones like that that also extend an extra several feet towards the ground. You would also need to buy columns capable of supporting the deck and whatever is above, rather than just the latter, which would be a lot more expensive if they were also ornate.
In your case it looks like there is one column, it's in the corner, there is a post in the corner, and if you are happy with the appearance of a 6x6 square column, most of those considerations don't apply.
But even then: Look at the "example" you posted. The beam, along the front, has to sit on top of the posts and you can see how it's notched into the posts in order to achieve that. If you extend those posts all the way to the ceiling, as they did, it means they have to be all that much bigger. That's more expensive, and also visually much heavier. Whether or not that matters is up to you.
That detail is better than the current detail. You save yourself the trouble of attaching twice at the deck elevation instead of just the once. You're not relying on the deck to stabilize the joint. Cheaper and better structurally. Beautiful.
I can't see enough of your deck to decide whether there exist many redundancies that stabilize your column with its current discontinuity. When you're doing your falsework versus demolition, remember that the current foundation-to-ceiling column needs horizontal braces at the deck elevation for stability.
In your example structure, I can see enough to notice a total lack of redundancies if they implemented your old connection. Using your old post detail and ramping up a horizontal force applied across the front of that structure, eventually the horizontal force would reach a tipping point where all of the posts tip over sideways ("tip under" is probably a better choice of words). The deck boards would provide a diaphragm that braces the front column line, where the tip over load is probably so large that it doesn't matter. Every time numnuts the homeowner decided to replace his deck boards, though, the tipping danger would return (and during such construction work is probably the most likely time frame when numnuts is going to apply that large horizontal load).
