They decrease the size of a transactions which will result in more transactions being able to fit into one block.
Yes, additionally :
1. Some of it allow shorter signature verification time, while BLS have longer verification time
2. Bellare-Neven and MuSig can be combined with Schnorr Signature for better result (with different method). Currently Bitcoin will use MuSig - Schnorr
3. MAST reduce script size by remove/don't include unused script parts (not compression). Additionally, it improves privacy as not all parts of script (which usually contain public key) must be submitted.
I doubt that storage could keep up if Bitcoin were to use, say, 1 GB blocks like some on the extreme end of on-chain scaling have been proposing.
I do agree though that storage is the lesser problem. More acute problems regarding blocksize are bandwidth and network propagation.
Storage speed and RAM usage also important when we're talking about block size/weight scaling. Looking at ETH, HDD isn't fast enough to keep up with all transaction and those who want to run full nodes must use SSD and it's RAM usage is more than average pc/laptop (at least 4GB, depending on client).