Good strategy on the upgrade

I gather that this is a MTB? First, you can verify if the bar is indeed steel using a magnet. Presumably the aluminum bar will be stiffer and lighter and possibly 'harsher' as a result of the stiffness. You may notice this while riding or you may not.

Are you finding your riding position uncomfortable? If so, then do you desire a more tucked or upright position? If not, then are you prepared to risk being less comfortable?

Switching to a bar with a 2" rise rather than 1" with the same stem will not change the distance to the bars but will force a more upright riding position. However changing the stem angle or length (or both) will have an effect on both.

Imaging you were to try steering by gripping the handlebars near the stem. The steering would be very 'quick' and 'lively' as a result of the shorter distance to the pivot point (the centre of the fork/stem).

Contrarily, a longer stem and/or wider handlebar will 'slow' the steering somewhat. Of course a wider handlebar can make heavy traffice more difficult to navigate, especially since they are at the same height as car mirrors.