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.
 A: change points
If you think there was a change point in 2010, then you'll get a better forecast by not using earlier data. The idea is that something has changed in 2010, and earlier data is irrelevant. So, by including an irrelevant information you make things worse.
The problem with this approach is that there can be another change point in future, and the model has no means to predict it. Prophet used to work like that when I looked at it a couple of years ago.
A variation of the idea is the regime change type of thinking, that your system switches between regimes, and you forecast accordingly. In this case you can predict probabilities of regimes, so it's a bit better than just assuming that the current regime will hold forever
exponential smoothing
A less arbitrary approach would be to weight the observations when estimating the coefficients of the model, e.g. the exponential weights so that earlier observations have lesser weight. This way you don't throw the old data out but its weight is lower than most recent data.
changes vs levels, unit root vs AR(1)
Is your data stationary? That's the question here to ask. Because, one way to interpret the historical data is that after the financial crisis, the housing starts dropped immediately but since then they were recovering to their balanced level of around 1,000. If this is the case then your first forecast seems more sensible, because you expect that the growth will slow down soon and there's a lot uncertainty as demonstrated with charts.
Your second forecast based on post-crisis data is what Greenspan called "irrational exuberance", that somehow housing market will be booming to infinity with much less uncertainty too. That's not a reasonable outlook
A: 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.
