I believe the purpose of the chain is to hold the flukes down to initially
set the anchor. Please correct me if I am wrong MW

The anchor rode, whether rope or chain, connects the boat to the anchor, but
the system really only works well (barring weird exceptions) when enough rode
is deployed to create adequate "scope".
Scope is the relationship between the length of rode deployed and the distance
between the bow pulpit and the sea floor.
In 20-feet of water, with a 5-foot clearance between the bow pulpit and the
surface, 75-feet of rode would create 3:1 scope- adequate to hold in
not-particularly challenging conditions. If there's enough space in the
anchorage, more boaters would prefer 5:1 for overnight moorage and
7:1 in a strong storm. In tidal waters, one has to consider the impending
changes in depth and allow for sufficient scope- particularly when anchoring at
or near low tide.

The greater the scope, the more horizontal the stresses on a set anchor will
be. Anchors are generally designed to "dig in" when pulled horizontally.

Chain is a "better" rode, in some ways, than rope. It is heavier, and can bang
up the foredeck worse than rope, but it tends to develop a heavy,
shock-absorbing belly between the anchor and the boat. It takes a lot more
pressure from wind or current to
straighten a chain rode than a rope in most situations. (Try stretching a
fathom of rope and then a fathom of chain. See how long you can hold your arms
out with one vs the other. Same thing goes on underwater) The chain tends to
lay flat along the bottom close to the anchor.

Boaters who routinely anchor in very deep water tend ot favor all chain rodes.
The chain rodes generally do not require as much scope to hold.

A combination rode is also a popular choice, with a length of chain
(traditionally equal to at least one boat length) spliced in between the rope
and the hook.