> they don't want American hardware / US influence shaping geopolitics in their backyard
It's more about alternative form of gov't, liberal democracy, that happens to have US as the predominate support base. They like to say it is the US as a single country, but really it is liberal democracy, aka "The West".
IMO not really, liberal democracy isn't that worthwhile/threatening - despite what US/LIO crowd likes to tell themselves. Many US partners in MENA are authoritarians with high income/comfy life. It simply pays better for many to align with hyper hegemon interest and be in good graces in last 50 years. Liberal democracy is only threatening in the sense it's open to US elite capture, US having inserted itself deep into political superstructures of many countries early on, turned some LIO, i.e. US being wealthy hegemon is good at influencing/shaping elites who knows it pays well to be aligned with US interests. Whether authoritarian junta or a crown prince or demographic politician, the latter just tends to be much poorer and easier to influence/capture. At end of the day prepositioning US hardware in their backyard using local geography to collect intel and do containment is much more threatening to their actual interests than spreading LIO ideology/values which semi competent state power can restrain.
China and their belt & road is the same idea you attribute to the US, but from an authoritarian gov't. The USSR did similar. In other words, it's not the form of gov't that does this, but rather the strongest players.
China is also pushing their hardware into everyone's backyards to collect intel. Again, not an artifact of the type of gov't.
What is the biggest threat to an autocracy or authoritarian? Political alternatives
I didn't suggest behaviour it was exclusive to gov system - it's boring self interest calculus - US simply had 50 years of global hegemony head start and played the game better as strongest player coming out of WW2 relatively unscathed, so much so that they're in backyards of everyone, and not everyone wants status quo of such arrangement. When has political alternatives succeeded in displacing autocracies/authoritarians? Typically autocrats get replaced by other autocrats. Also plenty of failed liberalizing movements that reverted back to autocratic rule.
Getting autocratic systems to liberalize generally requires generations of proactive elite capture and shaping by active US influence/intervention, and condition enabling that is recovering from being wrecked post war where superior power can insert itself into local political structures to regime change (be it US or USSR). The biggest threat is physical attack followed political change compelled from external influence.
Political alternatives are easy to crush during peace time if state remotely competent, limit domestic sources of LIO influence, i.e. ban western NGOs. Flip statement around, what is biggest threat to liberal democracies? Autocracies that simply exist fine + liberal democracies that don't. Hence LIO interest trying to undermine autocracies. Many PRC nationals in west / naturalized citizens of LIO countries who experience dysfunction of "alternative" and conclude, no thanks.
It's more about alternative form of gov't, liberal democracy, that happens to have US as the predominate support base. They like to say it is the US as a single country, but really it is liberal democracy, aka "The West".