The most important function of asset prices is for valuing the assets as collateral for debt. Owners don't benefit from the income they can earn so much as from the leverage they can put on their assets. Add limited liability and you're set.

The brainless should not be in banking -- Willem Buiter

They can compensate for wage inflation by attempting to increase their wages. Wage control rhetoric is structured to make this seem plausible, and also to limit it 'for everyone's good.'

There's no equivalent narrative for asset inflation. A house price bubble is labelled an opportunity, not a tragedy.

As Mig says, the other critical difference is leverage - assets can be leveraged to increase their nominal value, consumer goods and services can't.

Politically, the difference leads inevitably to plutocracy - or possibly it starts with plutocracy and leads inevitably towards its maintenance.

Effectively, power is defined by discretionary spending. Asset inflation squeezes discretionary spending, which in turn squeezes the political and economic power of consumers while enhancing the spending power of the ownership class.

Wage 'inflation' has the opposite effect. With generous discretionary income, consumers have more choices about how to spend their time, and aren't limited to 'productive' work.

Another relevant point is that historically, wage inflation has never been the cause of hyper-inflation. Although it's not often stated explicitly, there's often the implication that wage inflation will lead to a run-away inflationary death spiral.

In reality, hyper-inflation always happens for other reasons.