ets function in forecast package does not detect multiplicative trend when growth is strongly autoregressive

I notice that when fitting exponential smoothing models with the ets() function in the R forecast package that a multiplicative trend is typically not detected if the growth rate is fairly strongly autoregressive. For example,

x <- cumprod(exp(arima.sim(model=list(ar=0.5), 500)*.01+.01))
ets(x, damped=F, allow.multiplicative.trend = T)

Will usually return a model with an additive trend. When growth rates are less autoregressive than a multiplicative trend is more likely to be detected.

What is the basic explanation for why ets() will usually reject the multiplicative model? What would be another way to detect if a time series has an additive or multiplicative trend (taking into account that the series may also have seasonality and all the other things that ets() considers).