Kamen Rider Decade ends up borrowing a Lock Vehicle because they apparently forgot that he has his own bike — or did Diend take it, like in the net movies?
While the reasoning the Showa Riders use to fight the Heisei Riders is flimsy at best, it does make a lot of sense that in order for #1's plan to revive the fallen Riders to work, he needed something that can use the Rider Lockseeds to make sure that they could come back to foil Badan's plan, and since Kouta has a Sengoku Driver (that draws power from Lockseeds), he had to make sure that Kouta was the last Rider standing in their skirmish so that ZX can use Kouta as a conduit to bring everyone back.
Some of the matchups in the actual final battle can invoke this:
Kamen Rider Wizard vs. Kamen Rider #2 — Gaim's predecessor against #1's successor.
Kamen Rider Fourze vs. Riderman — The 40th anniversary Rider for the 4th Rider ever, both having the power of equipping various weapons on their limbs. And remember who Gentaro's best friend was named for?
Then there's the fact that this isn't the first time Stronger and Blade have fought, they were previously matched in the Rider Battle tournament during All Riders vs. Dai-Shocker five years ago.
Haruto siding with the Showa Riders does make sense given their reasoning as to why they're fighting the Heisei Riders. After all, he and a lot of other people had to suffer a man's grief for his lost daughter and attempts to bring her back to life. He just didn't want it to happen again.
As Ichigo had pointed out, the depression over the deaths of friends and loved ones is what caused Badan to return. While he singles out the Heisei Riders, it does make sense, as they do have lost friends and loved ones, the most recent by that point having found out he killed his friend by the time the movie came out. However the same can be held true to the Showa Riders. Famous examples including Nobuhiko and Misaki, and as shown in the first Superhero Taisen, they haven't entirely moved on from it (Kotaro trying to coax the former into becoming good). Could it be that Badan was drawing from them as well, but they didn't know it because they believed they've moved on from it?