You could make it into a bookcase. Mahogany or another tight-grained wood would be better than oak.

Yeah, that's a 70's thing...

But it does serve a function: to limit your view of the kitchen counter (looks like perhaps your fridge went in that area).
Think about what you are going to see from the LR if it's completely gone. The side and back of the fridge just isn't very attractive.

Open can work, but you need to be looking at something that makes sense from the living room: A counter height seating area, for example.

If that's too much of a remodel, then you should consider different materials for a divider wall (ribbed glass in a wood frame for example would look good and still let light in from kitchen to LR). This could be a half wall - half glass or full glass panel with wood trim. BTW: Ribbed glass is kinda trendy in kitchen cabinet doors - so could you repeat the use of that glass in your cabinet door panels? Could be a cheap way to update cabinets without replacing them.

If you post a sketch of your floorplan/layout, showing the relationship of the kitchen to the LR, and where the half wall is relative to everything, that would help.

Here's a wall made of ribbed glass. Note: you could do a half wall and square panes of glass or any type of design that works with your home.

I think I'd just eliminate it---too narrow to be much good and seems it is not secure enough to be long lived.

I'm also curious about the general layout - is that a back door on the other side of it, and is there more kitchen on the other side? Are there elevation changes at all? I can't tell from the angle how far that bit of counter is from the wall and how much you room have to play around with - is that a portion of island?

I would say where to go with it depends in part on how much of an overhaul you are doing on your kitchen, what your budget is, and what your style preferences are. You could really put some DIY time into it and make it a nice feature by going with the bookcase idea, and have space for cookbooks, etc. on one side and living area books on the other, or if that is a back door turn it into some kind of shallow mudroom shelf type unit. But, if you have a lot of work ahead of you renovating a 70's style home and you're working on a budget, you may want to focus your time and energy on something else and just get rid of it.

I have to admit, though, I'm not as opposed to half walls as i used to be. It's probably not very stable because you tore out the spindles, so if you decide to keep it you could add one decorative column at the end to finish it off, it would divide the space in a modern way without obstructing a lot of the room, and provide the support it needs between the floor and the ceiling.

[Traditional Family Room[(https://www.houzz.com/photos/traditional-family-room-ideas-phbr1-bp~t_720~s_2107)

another from houzz

[Traditional Entry[(https://www.houzz.com/photos/traditional-entryway-ideas-phbr1-bp~t_741~s_2107) by Grandville Home Builders Rivertown Homes by Design

You could work with either of these ideas to make them more modern or cottage or whatever style you're going for. I just saw a picture somewhere today of a white kitchen with rustic wood columns on either side of the island, but I can't remember where it was.

The spindles probably stabilized it as it was never intended to be freestanding. If you are going to have a half wall, it needs to be built differently than a regular wall. I'd either remove it entirely and do it over, or I'd remove it, period.