Slackening the head angle changes the bike's geometry. The effect on handling depends on the method used to slacken the head angle!

There are 2 common ways to slacken the head angle (HA) of a bike.

A - Increasing the Axle to Crown distance (A2C) by installing a longer fork or a high stack lower cup, this will make the bike tilt backwards.

When you slacken the HA by increasing your axle to crown distance, you also:

Raise the front of the bike.
Raise the bottom bracket.
Tilt the bike back => resulting in a slacker seat angle.

To change your HA by 1 degree, you increase the A2C by approx. 1"

Each of the changes above have a negative impact on stability and climbing!

B - Changing the angle of the fork in relation to the frame = changing the HA directly.

When you slacken the HA by changing the angle of the fork, you also:

Lower the front of the bike.
Lower the bottom bracket.
Tilt the bike forward => resulting in a steeper seat angle.

Each of the changes above have a positive impact on stability and climbing!

Bottom line:
Lowering the bottom bracket and the front of the bike
while steepening the seat tube angle, negates to some extent
the increase in wheel base, hence keeping many of the bike's climbing characteristics while improving stability and handling!