Does the determination of the ergodicity of a signal force any changes in methodology?
The concept of space as used in the statement ascribed to Wikipedia is presumably that of the ensemble of all possible signals, not space as in "Space: the final frontier...".  In the absence of parallel universes in which different signals from the ensemble can be observed simultaneously, it is rare for engineers to determine that a signal is ergodic by comparing time averages to ensemble averages.  More commonly, signals are assumed to be ergodic so that the values of time averages can be used as estimates of ensemble averages.  For example, an engineer takes $1000$ samples of a stochastic signal and plots a histogram of values.  This looks vaguely bell-shaped and so the signal is modeled as a Gaussian random process whose mean is the mean of the $1000$ samples etc.  Ultimately, the proof of the pudding is in the eating.  If this Gaussian model leads to predictions that differ wildly from observed results, the assumption of ergodicity might be discarded, or maybe $10,000$ samples, or $100,000$ samples might be tried (for example, predicting traffic at $5:30$ pm based on observations of traffic between $2:00$ am and $3:00$ am is rarely accurate, but 
observations over several weeks might lead to a better model).