If you're unsatisfied with merely having more, and only care about how much better or worse you're doing relative to everyone else, then you can make anything zero sum. The fact that you can do this with GDP isn't particularly interesting or revealing.

The GDP grows over time. Yes, we're still dealing with economics based on scarce resources (relatively speaking). That won't change unless we have a technological singularity, and even if that happens, some things of value like land (preferred locations) or esteemed original art pieces will still be scarce commodities.

What's the alternative model? That the government allocates the scarce resources instead of the market? What makes government better at this for most things (allowing for some exceptions)?

That's entirely artificial. At the individual or company level, nobody knows or cares about their percentage of GDP.

The economy definitely behaves in ways that has to do with percent of GDP. Capital allocation is the most obvious factor. Individuals feel the weight of finance on the economy regardless of whether they know it or care.

It's just not capturing anything interesting about how growth in one industry should affect other people's decisions. Consider a factory town in the Midwest. The factory closing is not good for other businesses! Their loss is not a gain for you. Or if some bank decides to put its headquarters there, that is very good for the community.

Generally speaking, being in a rich or growing area is a good location for business because your customers spend more. Similarly, a thriving economy is good for business, not bad.

You aren't going to convince people that good things are actually bad by measuring things in percentages. You're just measuring it wrong.

On the other hand, housing when there's no way to build more units is an example of something that can actually be zero sum. If you move in, that means one less place to live for anyone else.

You're talking as if all economic activity involves building things. That's not the real world. The main question we should be asking about growth is "what happens to productivity gains?" Do they accrue to everyone evenly? Or do they disproportionately accrue to a small number of people?

It turns out that over the last four decades, the answer has overwhelmingly been "accrue to a small number of people", and most people have seen almost nothing in terms of gains. A big part of the reason why is that there are entire industries (finance) devoted to that accrual. As a result, the continually-growing pie doesn't matter, because every time the pie grows larger, a few people keep taking larger and larger slices of it.

GDP ain't fixed.