Is it reasonable to choose a subset of the time series to create a model? I am new to time series forecasting and would much appreciate your reply. I have an annual housing starts data between1970-2022 shown, below.

I want to forecast the next 10 year housing units. If I use the whole series to model, the prediction interval is quite wide, below.

Based on a very similar project is here (https://towardsdatascience.com/applied-time-series-forecasting-residential-housing-in-the-us-f8ab68e63f94) I tried the last 12 year as predictor  and I get better accuracy, below.

But, is  choosing only last 12 year for modelling reasonable? I am concern that my model doesn’t capture the evolution of the data if I don’t use the whole series. Any suggestions? Thank you in advance.

I would not say one forecast is "more
accurate" than the others. You will only see that after the fact.
One forecast does have narrower prediction intervals, but only by pretending that everything longer than 12 years back is completely irrelevant. I find that very dubious - housing follows the business cycle, and there simply are ups and downs, and just eyeballing things, I find it highly unlikely that the positive trend from the last 12 years would continue. Note that there is already a small dip at the end of your history. Right now, it looks like there won't be a deep recession, but it's still a possibility, in which case new housing starts will rather go down than up.
So if you want to go with a pure time series method, I would definitely prefer using the full history, because that gives you a more realistic picture of the residual uncertainty - the bottom plot is just unrealistic (extrapolating an upward trend) AND overconfident (too narrow prediction intervals). And of course, "serious" forecasts of housing starts probably involve macroeconomic data and additional assumptions about how the business cycle will play out.
