The best way to put an emphasis on ground game is to increase hitstun and shield stun. Grounded stun needs to increase, and shield stun must be substantial.
A lot of traditional fighting games balanced out blocking and attack strings: It's called advantage on block. Take tick throws in Street Fighter for example. A tick throw is when you throw out a quick normal, then quickly walking up to the opponent and grabbing him. For a character like Ryu, a common set up would be a crouching light punch, walk, then grab. This works because, 1. The attack comes out fast, and the cool down is fast and 2. There is enough hitstun from the attack so that the opponent will be in a defensive position until Ryu is within grab range. Using a move such as a crouching fierce on block cannot produce the same results because the stun on block produced isn't enough to supplement the cool down of the move. In other words, the opponent will probably be out of stun, and you will still be stuck in the attack animation, leaving you open to a punish.
So, how can you implement a similar system in smash? By increasing shield stun, but keeping the current shield drop speed, and also introducing adequate push back on shield for attacks.
Keep in mind that in traditional fighting games, there is little to no cool down from leaving a defensive position, so in theory this should balance things out. If a character like Fox or Mario jabs your shield there should be enough stun on shield for you to be able to be able to initiate a grab, but by the time your attack ends, your opponent can respond appropriately, possibly by dropping the shield and jabbing him out, or with a character like Megaman , an up tilt, because it comes out instantly, and can possibly punish the opponent if they decided to throw out a tilt during the block stun.
For example, let's say Marth is using one of his safer aerials on a shield opponent: a SH Nair. If the move tips the opponents shield , it does a solid amount of stun, but it pushes the opponent back a good deal, enough that the opponent would be able to follow up with something like a Forward smash without advancing. You can dash in during shield stun with a dash attack or a dashing dancing blade. It you tipper the dash attack, the opponent will remain in shield stun, but the cool down of the attack vs the stun will put you and your opponent in 50/50 position, and since the dash attack pushed the opponent just out of range of most of your normal attacks, you can use shield breaker, which can be punished. So if your opponent responds accordingly he can roll, jump or spot dodge. By this logic, the safest option would be opting for dancing blade since it's guaranteed pressure, but it has significant cool down and Marth steps forward during the attack, so unless Marth opts to use the down variant of the move on the third attack(which makes your character step backwards), your opponent will definitely be able to punish you. Your choice of attacks in this situation dictates how much pressure you can put on your opponent and your ability to gauge whether or not you should play with tact and space your moves or just go for the automated cop out. With shields being able to drop so fast, your opponent will be able to do more than shield grab or up B out of shield.
Fixing smash's ground game all depends on how they tweak the defensive options.