You would have to be careful to avoid a CCJ resulting from this.
You certainly shouldn't simply ignore them, no (but then again you shouldn't simply ignore a summons to Court or a bail date given after charge, otherwise you could just as easily be found guilty in your absence, be fined and have the fine registered as a debt).
You are misinterpreting what a Fixed Penalty Notice actually is. If they did not exist, the system would be this:
1. You kick off or whatever commit whatever minor offence it is.
2. Witnesses - door staff or whatever - see what is happening and call the police.
3. Police turn up. They have not seen what happened so they ask the witnesses.
4. If they believe that an offence has been committed, they report you for summons or arrest and charge you (and if they do you get your prints, DNA and picture taken and kept).
5. You go to Court. If you plead guilty they fine you up to the maximum (lots more than £80) or give you some other sentence. You get a criminal record (this bit is important too)
6. If you plead not guilty the witnesses (the door staff or whatever) come and tell the Court what happened, you give you account and the Court decide whether you are guilty or not.
With FPNs everything is the same until stage 4. There the police have another option - they issue a FPN. There are then two additional stages:
4a. If in the 7 or 14 days or whatever you have to decide, you decide you committed the offence and are guilty, you pay the fixed penalty notice and that is the end of the matter - no criminal record, no prints/DNA/photo taken, no time off work for meaningless court hearing only to plead guilty.
4b. If you decide you are not guilty, you fill in the little slip and the police / CPS decide whether or not to summons you for the offence. IF they do (and they may not), continue just as before from stage 5.
If we take the police out of the equation in issuing the FPN there is absolutely no difference to the rest of the sequence - it simply does not involve them turning up, listening to what the door staff of whatever say and then issuing a FPN
entirely based on that account.
It is worth noting that the Magistrates main concerns seem to be that people who should have been arrested, charged and brought to Court and sentenced to way more than an £80 fine would not be dealt with seriously enough! Not that people may be treated too harshly!