For instance, if all the DNA of all organic life is altered, the precision required to do that for all organic life would be almost impossible. Does it just rearrange DNA? If not, where does the matter necessary to add base sequences to the DNA come from? How would the Crucible/Catalyst distinguish between life, if it recognises synthetic and organic life? What would the consequences be if all life was fundamentally changed in one instant? If all the cells in your body had their genetic information changed, it's possible that you would just die. The new DNA would have to be "backwards compatible" with the biochemistry of your cells that express that genetic information.
This.
While it's true that we in the real world do not know everything (yet), we still do know a good deal... enough to mark determinate things as bill schitt (it should be fairly easy to deduce what does "bill schitt" actually stand for).
If something straight up contradicts what we know then you can't just handwave it with "it's an incredibly advanced tech": it doesn't work like this, it still is magic.
The most awful thing about Synthesis though is, in my opinion, that even if it wasn't impossible, it would still be bill shitt.
Just think about it: the tech that produces synthesis is actually handwaved as a technology advanced enough to
1. alter all the DNA of all living beings
2. alter the DNA only, in a very specific way, without being disrupted, blocked, or modified or corrupted by barriers, metal plates, magnetic fields etc., and without killing nor damaging the owners of said DNA in the process
3. adapt to all the various DNAs (which vary wildly even if you only consider the species on Earth - if you include aliens too, then the variation would very probably be immense, even if only to account for dextro- and levo- biologies) in a way that induces the same intended result in everybody
4. have the new DNA be still compatible with the biology of the host, or even have all the molecules in every body change too in a very specific way that allows both the change and compatibility (which alone is an infinitely complex thing to do)
5. whatever bill schitt it was said about doing the same to synthetics, which don't have nor require nor can use DNA in any way (!!!)
Really, if the Reapers had a technology anywhere near this advanced, one would wonder why did they even bother with physically harvesting, with indoctrination, with the Collectors, with the Geth heretics, or even with leaving Sovereign behind at all...
Even justifying it with tremendous energy costs, with a tech that allows to act in such a complex way over enormous distances with such a precision and with no possible effective protection whatsoever they could have simply indoctrinated everyone everywhere at the start of the invasion while also directly testing the cycle's "readiness" and then take their sweet time with the harvesting, and it would still have required less power than what they actually use to overcome any cycle's resistance.
(Consider even just how much power is wasted to move around the Reapers' and the cycle's forces, and how much is wasted fighting, all of which would end up unused if they indoctrinated everyone immediately, only to release control if they were found "ready for synthesis").