Ok, who says it's the goal of every bassist to cut through the mix? There is also, for example, the school of thought that bass should be felt rather than heard. While I don't agree with that school of thought because even the fundamental of of my E string, or my lowest frequency at 41.2 Hz, is still in the human high fidelity hearing range (which extends down to 20 Hz), I do respect that idea and players who choose to approach the instrument that way.
I'm not making any assumptions about whether Mark Hoppus intends to cut through with his bass tone or not, but we can't call someone else's tone crap simply because it does not achieve what we would like to achieve with our own tones. We really don't know what Mark Hoppus intends to achieve with his tone. Sure if it's his goal to cut through, then Mark Hoppus' tone clearly sucks, but I don't think we should make the assumption that every bassist intends to cut through with their tone.
By 'Cut Through' I mean, Be heard. Sure, if you are of the thought of Bass is supposed to be Bass, then crank it, be in that low range. If you don't have a keyboardist or a synth player, I'd be willing to be that you are in your own range with that, so you occupy that space of the mix, and you are heard. I happen to love Doom music. And part of that is nothing more than droning right in that 20Hz range. But its cutting through the mix. I can hear that, as well as drums, and the guitars above it. See what I'm saying?
I cannot picture any bassist, other than one who is highly self conscious of his playing, that would actually seek out and attempt to be buried in the mix, in any sense.
And I'm not saying anything about Mark Hoppus. I am a Blink fan, but that's because its catchy, fast, and generally very lax in nature and comedic to listen to, certainly not for Mark.
Well I also wanted to point out that, if it is the desire of a band to have the bass cut through the mix, then the guitar players have to make room for the bass, somewhere. The bass not cutting through is as much a function of less than optimal guitar tone as it is less than optimal bass tone. It's easy to point the finger at the bass player when he's not cutting through but the guitards are to blame as well!
But I've addressed this point in my statement above. A band that is not willing to work together with the EQ is one that is surrendering itself to a crowded mix. I'm not attempting to bicker with you Mark, but I personally find that we wave the 'Bloody Shirt' of guitarists a little too much around these parts, just as much as we are quick to point fingers at the bass player. Its not a sole responsibility. Its the bassist, the guitarist, the drummer, and especially the producer, which is one we often fail to mention at all. This has turned into a blame game for no reason. Everyone that touched the mix is to 'blame,' so really no one is to blame at all. Its something that I and many others find to be a fault of the music that everyone at every stage of production was apparently satisfied with.
So OP: If you really just want to be Mark Hoppus, sure, seek out the EQ settings that will get you buried in the mix. But if you want the sound you hear when you actually hear him (i.e. with Tom isn't playing), work with your band mates, follow all of the advice above that isn't tinged in sarcasm, and I'm more than willing to bet you'll get as close to his solo tone, full on in a mix, as you otherwise could.