Interesting observation, but I think the answer is partly explained by several factors:
First, any calculation of real GDP would eliminate the year-over-year variance that could be due to taste shocks leading to significant price changes.
Second, I think your observation is partially true, however. What makes an iPhone more valuable than an old Motorola smartphone? Sure, some inputs might be slightly different, but the "production technology" of the iPhone makes it such that we (in general) do value it higher. While some measures like CPI try to account for some of those issues by considering benchmarks for certain performance criteria (like processing power, memory, etc.), in the end, there absolutely is some taste-based component.
I think it's partly accounted for by aggregation, as you mentioned, but I think the third point is that there's a bit of a disconnect between what value is trying to measure, and what GDP is interested in. Theories of value attempt to explain why we attach certain "utility amounts" to different goods. But that doesn't mean the output of any particular "theory of value" is subjective: the observed prices and quantities are quite objective. GDP (like other macroeconomic indicators) is more interested in tabulating those objective outputs of the theory of value and observing their change over time.
For example, I know I value the green mechanical pencil in front of me at \$2, despite the fact I only paid \$1 for it. Assuming the production costs are negligible, GDP would observe that as \$1 of economic activity. It doesn't consider how much I would have paid for it, which is what different theories of value attempt to explain. Furthermore, why I value it at \$2 might be for any host of reasons- perhaps its a subjective value, or perhaps that valuation reflects what I think the pencil will be worth in a year's time. Regardless of what that reasoning is, the objective measurements that GDP considers are the price paid and quantity.