"Inherently flawed concept" only applies to the standard of boss rushes that fangames are using today, such as the K3 or Z3.
Boss rush, by design, is a series of boss fights that you need to accomplish before continuing on. There are multiple ways to approach this concept, and the most popular way of approaching it is the one that is frowned upon the most.
"Traditional" Boss Rush - A series of bosses (that may/may not have a save before/after each boss) that you beat before continuing. This is what is seen in games such as K3 and Z3, and have way too high of a difficulty curve to progress at any decent rate. The difficulty of these boss rushes is typically so high, it takes the player 10-40+ hours for each boss, with some going well beyond 40 hours (see: Piano in K3). This is probably not the best way to go about boss rushes, but is the most traditional, reminiscent of the Megaman series. If you do choose this method, you need to nerf your bosses to a point where they are easy enough to beat within a short amount of time. However long it takes the player to beat the platforming should not exceed how long it takes them to beat any particular boss, more or less.
"Target Score" Boss Rush - A series of bosses that have different point values assigned to them. A door will unlock after X amount of points, allowing you to progress past the boss rush without having fought all of the bosses. This is well done in "I wanna be the Crysis", where you have to score 25 points to get past the boss rush. Harder bosses award more points, and vice-versa for easier bosses. This is a much more player-oriented way to go about boss rush, as it allows the player to pick and choose what bosses they want to fight. A major disadvantage of this style is that it typically requires a large number of bosses to pick from, which is opposite of what you had planned for your boss rush.
"Lottery-Style" Boss Rush - A series of bosses that are randomly chosen from a pool of bosses that must be fought in some order. There may be a varying number of bosses to fight, or there may be only a select X number of bosses to fight out of a pool of pre-determined bosses. For example, if I had 6 bosses, I can have the player randomly "roll" 3 of them to fight. I could also potentially give the player 1 or 2 "re-rolls" for any boss that they think is too difficult/they don't like. I like this boss rush the most, but I only see traces of this boss rush scattered throughout games, typically through platforming instead of bossing. For your game, out of 3 bosses, you could have the player roll 1 or 2, with possibly a re-roll for one of them if the player really does not like that boss. Maybe the re-roll could be a secret item in your game, or a reward.
This is how I see boss rushes. I don't believe boss rush is an "inherently flawed" concept, rather, the traditional style may not suit fangames to the liking of the majority of players. Thus, tweaks are required from the traditional boss rush to better suit fangames and the player himself/herself.