In murder cases this is done by low level forensics at the scene, did they try and scrape the area for DNA around where the phone was found? Footprints ? If it was wet someone must have been able to destinguish between a fresh footprint and one that had been there say 4-5 days ? Any clothing that may have got caught on something ?
If it is foul play and she is found somewhere and maybe the police have a weak lead on a suspect but want to strengthen it they are going to need that evidence , early evidence
You are not going to be able to do 'low level' forensics on an outside scene where you really don't have much of an idea what you need to look at and for what.
Even the 'mainstream' (not low copy number which is what I assume you are talking about) DNA profiling method currently in use,
DNA-17, is very sensitive and as such extensive precautions have to be undertaken to prevent cross contamination. DNA techniques are useful where you clearly know what you are looking at - a item of clothing, blood splatter, something handled by someone. Such techniques are not suitable for examining whole areas of ground. You generally need a swab taken from a discrete area to test.
Footprints are generally only useful if you have something to compare then with and on a tow path, which I assume gets a reasonable amount of foot traffic, it would not be possible to do anything meaningful.
Forensic use of footprints is useful in circumstances where you have a small area to examine with clear footprint where you would not expect a mark to be left normally (say at the back of a flower bed under a window that was a broken as a point of entry for an offence) and suspect arrested with the footwear obtained for comparison.
How on earth do people imagine you are going to protect what would presumably would need to be a large stretch of river bank from the elements whilst you slowly inch along it looking at any apparent footprints?
And what effect do people imagine this would have on other lines of enquiry that could not be progressed until the 'footprint sweep' had been completed?
And again lets say you recover some footprint impressions... what are you going to do with them?