A two week (2016 blocks) forced signaling phase has two major advantages.
Firstly, it offers a signal to the network that miners will be enforcing the soft fork rules in the next phase following the forced signaling. It is an imperfect signal as miners could follow the forced signaling and then not enforce the soft fork rules but it is better than nothing. To actually do this would suggest maliciousness or incompetence.
Secondly, it presents the possibility for mined blocks that aren't signaling being rejected in advance of when soft fork rules are supposed to be enforced. Not only does this provide an incentive for miners to signal (their mined blocks could get rejected otherwise) but it attempts to, temporarily until they agree to enforce the soft fork rules, kick them off the network so only miners that are enforcing the soft fork rules are on the network post activation. The whole point of soft fork activation is to attempt to coordinate across economic full nodes (and miners) a block height for when soft fork rules will be enforced from. We attempt to do everything possible to provide clarity to the network on what this block height is. In a scenario where miners have failed to meet the signaling threshold for a long period (e.g. a year) forced signaling is an important tool in the toolkit. If miners meet the signaling threshold in advance of the forced signaling it obviously is not needed.
Luke Dashjr stated on IRC:
The primary purpose is to definitively indicate the soft fork is active on the chain. While it still relies on enforcement, this ensures there is no dispute over what the correct rules are. As a side effect this also makes it easy for any group of dissenters to reject the new rules. The intent of a soft fork should never be to literally force new rules (upon dissenters)
(Luke is referring to dissent against the soft fork rather than dissent against the activation mechanism set in a Bitcoin protocol implementation.)
David Harding added that MUST_SIGNAL forced signaling has additional value in a scenario where there are both BIP 8(LOT=true) and BIP 8(LOT=false) nodes on the network. It ensures the soft fork activates for nodes setting LOT=false when the majority of the network is setting LOT=true.
I run a node with LOT=false; everyone else runs a node with LOT=true. At block xxxxxx, y'all start enforcing taproots rules, but I never saw any signal, so I continue treating taproot transactions as anyone-can-spend, which is bad for me personally. If there are a lot of people with LOT=false, it also makes it unclear whether taproot is really being enforced, increasing the risk that miners may try to steal funds sent to taproot outputs.
In addition David Harding argues that forced signaling is not particularly dangerous.
What makes forced signaling so dangerous? We had that with the BIP34, BIP66, and BIP65 forks. Except for a hiccup with BIP66 due to spy mining, I don't think there was any problem. BIP8 forced signaling is also only required for a brief period, so any disruption should be short
Comparing a forced signaling phase to a flag day was discussed further on this BIP PR.