This is a somewhat plausible idea, but serious balancing issues come into play with such a complexity within Ridley's moveset:
For instance, you say that both of these modes would last for a "short time"; in this way, a major concern is raised by the fact that he will have yes, a short time interval for his powerful, "berserk" mode, but also a short cooldown, meaning Ridley essentially alternates between the two modes since both mode times are "short."
Further balancing issues exist as well. You say that beginning players would "waste" their berserk mode time by attacking players and then go into a cool down mode, however this raises serious questions: Since Ridley is in this "berserk" mode, shouldn't he be powerful to the point where he could break through shielding players, exemplifying the value and power held by this mode? If even in this mode he doesn't have amplified strength to the point where he could break shields, then Ridley becomes essentially a bottom-tier character at best. After all, most AVERAGE players will know to constantly shield, run, evade, etc. in order to avoid the threats of something like Ridley's "berserk" mode. Again, this would thus cast Ridley down to the very bottom of the tier list, since his "berserk" mode could be easily avoided by simply running away and then having him easily punishable while in cool down (especially since both modes are time-based). So really, the flaw of this gimmick is that Ridley will either be ridiculously broken, or so vulnerable that he would be one of the worst in the game, a set with such extreme power and drawbacks at the same time would be very difficult to balance properly.
Going back to the "boys from men" thing, Ridley would have to be made EXTREMELY powerful in his berserk mode in order to counterbalance the harsh vulnerability he has while in cool down, this would mean that he would have to be fast to the point that he could easily chase down any character that would try to evade him, making him broken. With regards to his cool down, if he is vulnerable such that he is slower and that his shield can be easily broken, this combined with the extreme power he holds in berserk mode would ultimately make matches all around bland. Because of the extreme nature of this moveset, matches against Ridley would essentially become hit-and-run K.O trades which would become monotonous in a very short amount of time. All the match progression would be is:
a) Match Starts, Ridley K.O.'s in berserk mode, enters cooldown as opponent respawns
b)Opponent retaliates easily K.Oing/gimping Ridley as he waits for his cooldown to end.
c)Repeat steps a and b.
Or:
a)Match Starts, Ridley and opponent play cat and mouse for 8 minutes as they try to take advantage of Ridley's berserk/cooldown times.
Ultimately, the extremes of this moveset prevent it from being very easily balanceable and thus if such a moveset was given to Ridley, he would either be broken to all hell or at the very bottom of the tier list. Not only that, but matches would become overall monotonous as players played cat and mouse in order to avoid the very possible K.O. trade scenario that I mentioned. So really, the only way I could see this working is in Ridley dittos, where potentially both players could be in cooldown at the same time and have to improvise (but everyone playing Ridley would inevitably become boring as well)
Overall, I would much rather go with the "glass cannon" playstyle that @
False Sense
mentioned where Ridley could have extreme offensive potential but at the same time be on the middle/lightweight end (with some other vulnerabilities) to balance his strong offensive power.
Thank you for reading.