Home Alone is a franchise that should've stopped right at Home Alone 2: Lost in New York (1992) the moment the producers were unable to get a teenage version of Macaulay Culkin as Kevin for Home Alone 3, so they had to revolve the third one around a little known boy named Alex Pruitt who is not on Kevin's level in terms of star power.
Plus, instead of dealing with Marv Murchins (by Daniel Stern) and Harry Lyme (Joe Pesci), we're now dealing with Peter Beaupre, Alice Ribbons, Earl Unger and Burton Jernigan as the four spy criminals from a Hong Kong terrorist organization set on wanting some expensive microchip for their own nefarious gains in Home Alone 3 (1997).
And while Home Alone 4 did go back to the McCallister family, it wasn't the same. It felt like Michael Weinberg was too obnoxious to be like Kevin, and it was supposed to be Marv's time to shine, only it's not the Daniel Stern version of Marv we've been accustomed to in the first two Home Alone films (we get the skinnier, shorter and cuckier version of Marv), he also has a wife Vera instead of his tag team partner Harry, and so it really looked nothing like the McCallister family like in HA1 and HA2, while Home Alone 4 bombed and thus is considered to be the worst Home Alone movie ever, along with the 2012 Home Alone movie with the Baxter family.
So no, I don't think Disney should've taken the rights to Home Alone. In fact, Home Alone should've been buried after HA2: Lost in New York, just like how Killer Instinct should've ended at Killer Instinct 2 (1996).