Both Catholicism (even with the pope) and traditional Protestantism have mechanisms to resist this. Catholicism resists it because clericalism pushes back against cults of the person of the pope specifically (notice the incessant factional backstabbing), but also because the parish priest is more a functionary of rites than anything else--sermons in Catholic churches are generally brief. Protestant denominations like Presbyterianism, Methodism, and Lutheranism maintain (at least nominally) the Catholic tradition of apostolic succession and a system of Presbyters and Bishops, which diffuses theological power structurally. Notably Anabaptists and Pentecostalism discard these structures almost entirely, so no coincidence that they're more susceptible to cults of personalities.
I grew up Catholic in a small southern town. There was one Catholic church among dozens (if not a hundred plus) protestant churches; it was mostly attended by military families. I remember the parish priest (who was my confirmation sponsor as I had no family or close Catholic family friends to sponsor me) complaining that the community, including parishioners, gossiped that he wasn't godly enough. He drove around in a Cadillac and drank (moderately). What the community didn't know was that he was pretty much the only pastor who personally volunteered at local charities unaffiliated with our church, in addition to the work he did for the church's own programs. But he never made it a point to inform people of this because he did it on his personal time--just like he bought his Cadillac using his clerical stipend and drank on his own time. He refused to advertise this on principle. He railed against the cults of personality of local churchgoers (including his own parishioners) and of local churches. Their priorities were all screwed up. Since then American Catholicism specifically and Roman Catholicism globally has increasingly shifted in this troubling direction, in tandem with Christianity more generally.
Anyhow, to reiterate, it's not just a problem with Baptists or Pentecostalism, nor do all Baptist and Pentecostal churches suffer from the problem. But there's an interplay between doctrine and institutional structure. People will readily admit it when discussing how the Roman Catholic hierarchy protected child rapists; but they refuse to see the downsides to excessively decentralized institutions that put too much unchecked power and influence in the hands of local leaders.
The U.S. has exported the problem globally because it's exported the Charismatic Movement.