To support Genghis and Gertrude, we generally use indicated airspeed (IAS) for two things in flight, and they are surprisingly unrelated.
The first, where GPS is a great substitute, is obviously "when will I get there?". Use GPS for this. The IAS is affected by numerous factors in cruise flight (wind being the greatest) that GPS is superior anyway.
The second is the relationship between the air passing over the wing relative to the air required to pass over the wing for the given flight condition. ASI is pretty good for this, up to a certain pitch attitude, though even after that it's giving information which will help you to stay safe. GPS is not at all good for this, the GPS speed does not consider the affect of wind over the wing, and the information can be harder to interpret quickly, relative to the rate at which the airspeed can change in those conditions of flight. The GPS will, also not be positioned in your scan, where the ASI is required to be seen, so you'll be searching the panel for it when you should be looking out the windshield.
Interestingly, I was flying the Tiger Moth a few weeks back The rear cockpit (where I was flying from) ASI was actually annoyingly close to me to see easily, and it's antiquated markings difficult to quickly interpret. The front cockpit (no one up there in my way) ASI was easier to see, but I think out of calibration by quite a lot. The wingstrut mounted spring on was there, and seemed to work well, but ultimately, I just flew by feel, and that worked best. Now I was not going on a cross country, so navigation was not a factor.
In the same period, I was also flight testing a Siai Marchetti 1019A. For a rather advanced turbine powered aircraft, which has fairly high wing loading when heavy, I was amazed to figure out that it has no stall warning system at all, and only a three knot margin between the first indication of a stall, and the break. It also had very unusual pitch forces near the stall (sometimes reversing = very poor "feel") This drove me to watch the IAS fairly carefully on approach and departure.
For the certified GA aircraft, any can be happily landed without any reference to the ASI, with a bit of practice. I highly recommend this be done by every pilot recurrently - it's going to happen to you sometime!
