I don't think they would be issues at all...I think you're coming from the magical angle? I just don't think their brand of magic is powerful enough to beat dd
While that may be true for the most part, every time Doomsday pops up he is always portrayed as a major threat. For instance, even the Luthor-cloned version of DD from AC smacked around multiple solar-powered Kryptonians (inc. Superman and Kara), and tanked their collective HV. It was only when a dozen (or so) of them ganged up on him that DD was beaten.
...And H/P is considered far and away superior to these 'no name' incarnations. Point being: I think H/P would do just as well now as he did back then. His effortless trouncing of Darkseid is a bigger feat then most realize, imo. /shrug
I feel that the gap displayed between H/P DD and Superman alone has been closed quite a bit due to Kal's better feats. And people like Hal, Captain Marvel, Diana, etc, have likewise gotten either more powerful through explicit upgrades, or just have been portrayed with better feats since the 90s. I think, truthfully, Doomsday would be a threat to the team, but to the degree where he could take them all on at once and possibly win? I just don't see it, personally. I agree in team busting on panel to a degree, but then when someone (ie. Superman) is able to contend for an extended period of time against said team buster on his own, it somewhat ruins the validity of it.
Superman's feats tend to disagree with you. Perhaps it's a bad example as it is Superman (who tends to go above and beyond when plot calls for it), but Superman has a storied history of being on a team and getting roughed up by someone and then standing up to that same threat by himself later on.
right...hence all the more impressive that HP DD was the one foe that truly scared him to the core, the one foe he did not think any powerup would help him beat, the one foe he had to send to the end of time to win
And Superman later turned around and got over his fear of Doomsday and his "death" at his hands.
Doomsday was designed, introduced, and intended to be the ultimate enemy for Superman, and not just physically, but emotionally and psychologically. Physically, he's still a beast, but those emotional and psychological advantages he had over Superman don't hold up to the Superman of today (or yesterday as it were). He considers DD a threat, obviously, but he's not frightened of him or scarred by him.
Barring plot device amps and hyperbole and focusing on actual feats, Superman does tends to shine better on his own than if he's with the JLA or a bunch of Kryptonians, etc. He's not exclusive to this, but it's something cataloged in comics. Call it inverse ninja rule or whatever, but that tends to happen a lot.