Outside of providing a little more live-fire practice in amphibious operations before 'the big one', not really.

The Italian campaign had two positive effects for the allies, and one potential negative effect which required keeping an eye on. The two positives were, firstly, as you mention, causing the Germans to keep troops in Italy instead of France, and also when the Italians surrendered once the Allies were on the boot, the Germans additionally had to garrison all the former balkan areas such as the Greek islands which the Italians had been garissoning. This led to a little discussion in Allied headquarters as to whether or not they should garrison the Greek islands, given that ownership was strategically advantagous, but eventually it was decided that they would be left alone, that troops couldn't be spared. The other positive was, of course, knocking one of the Axis out of the war.

The issue of not enough troops was the big concern particularly with the US senior staff. Operations in Italy were always seen as a diversion from the Northern France invasion. This meant that when they were allocating materials, particularly landing craft, but basically anything from units through supplies, the priority was always Normandy, and the Italian campaign basically got whatever was left over. For a couple of years, US high command was worried that the Brits would want to shift focus from France to 'the soft underbelly.'

I would suggest that you should also study the divisions both side committed to this front; i am not sure what the recent research is but back when I studied this it was not at all apparent which side was gaining strategic benefit by tying down the other side. There are times when it can be argued the Germans were actually succeding by sucking more allied troops into this theatre then the Germans had. But both sides were constantly changing their commitments here so you have to study the numbers carefully.

It should also be pointed out that the Anzio operations tied up lots of shipping in this theatre and may have had some effect on the timing of the D day operations. Some of the shipping used in Anzio was re directed to the England are if I understand correctly.